exp_first_half – Complete Experiment Report

Base

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Base_Gaussian (MvNormal, mu, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) -0.537 0.594 -0.165
SMC (0.0, 0.0) 0.020 0.984 0.008
Metro (0.0, 0.0) 2.980 0.00561 1.326
DEMetro_Z (0.0, 0.0) 3.865 0.000571 1.819
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -4.373 0.000327 -0.978
Metro_vs_SMC 0 2.511 0.0213 0.561
Metro_vs_DEMetro_Z 0 -0.904 0.378 -0.202
HMC_vs_Metro 0 -3.323 0.00358 -0.743
HMC_vs_SMC 0 -0.549 0.589 -0.123
DEMetro_Z_vs_SMC 0 3.702 0.00151 0.828
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.021 0.022 0.010 -0.165
SMC (0.0, 0.0) 0.022 0.022 0.010 0.008
Metro (0.0, 0.0) 0.035 0.022 0.010 1.326
DEMetro_Z (0.0, 0.0) 0.040 0.022 0.010 1.819
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) 0.202 0.841 0.068
SMC (0.0, 0.0) 0.125 0.901 0.042
Metro (0.0, 0.0) 1.536 0.133 0.553
DEMetro_Z (0.0, 0.0) 3.258 0.00291 1.597
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.071 0.944 0.016
Metro_vs_DEMetro_Z 0 -2.059 0.0535 -0.460
HMC_vs_Metro 0 -1.950 0.0661 -0.436
HMC_vs_DEMetro_Z 0 -3.826 0.00114 -0.856
Metro_vs_SMC 0 1.233 0.232 0.276
DEMetro_Z_vs_SMC 0 3.102 0.00587 0.694
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.032 0.031 0.016 0.068
SMC (0.0, 0.0) 0.031 0.031 0.016 0.042
Metro (0.0, 0.0) 0.040 0.031 0.016 0.553
DEMetro_Z (0.0, 0.0) 0.056 0.031 0.016 1.597
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) -0.385 0.702 -0.140
SMC (0.0, 0.0) 0.095 0.925 0.043
Metro (0.0, 0.0) 4.788 5.65e-05 2.600
DEMetro_Z (0.0, 0.0) 8.376 1.02e-08 5.030
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.624 0.0018 -0.810
DEMetro_Z_vs_SMC 0 7.507 4.25e-07 1.679
HMC_vs_DEMetro_Z 0 -8.512 6.59e-08 -1.903
HMC_vs_Metro 0 -5.036 7.34e-05 -1.126
HMC_vs_SMC 0 -0.491 0.629 -0.110
Metro_vs_SMC 0 3.547 0.00215 0.793
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.030 0.030 0.005 -0.140
SMC (0.0, 0.0) 0.031 0.030 0.005 0.043
Metro (0.0, 0.0) 0.043 0.030 0.005 2.600
DEMetro_Z (0.0, 0.0) 0.055 0.030 0.005 5.030
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) -0.480 0.634 -0.155
SMC (0.0, 0.0) 0.109 0.914 0.045
Metro (0.0, 0.0) 4.130 0.000249 1.775
DEMetro_Z (0.0, 0.0) 6.247 1.27e-06 3.451
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.267 4.39e-05 1.178
HMC_vs_Metro 0 -4.372 0.000328 -0.978
Metro_vs_DEMetro_Z 0 -2.880 0.0096 -0.644
HMC_vs_SMC 0 -0.623 0.54 -0.139
Metro_vs_SMC 0 2.967 0.00792 0.663
HMC_vs_DEMetro_Z 0 -6.765 1.84e-06 -1.513
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.014 0.015 0.004 -0.155
SMC (0.0, 0.0) 0.015 0.015 0.004 0.045
Metro (0.0, 0.0) 0.021 0.015 0.004 1.775
DEMetro_Z (0.0, 0.0) 0.027 0.015 0.004 3.451
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) -0.608 0.547 -0.215
SMC (0.0, 0.0) -0.472 0.64 -0.184
Metro (0.0, 0.0) 3.288 0.00259 1.503
DEMetro_Z (0.0, 0.0) 3.985 0.000512 2.375
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -5.045 7.19e-05 -1.128
Metro_vs_SMC 0 3.579 0.002 0.800
Metro_vs_DEMetro_Z 0 -1.307 0.207 -0.292
HMC_vs_Metro 0 -3.514 0.00232 -0.786
HMC_vs_SMC 0 -0.094 0.926 -0.021
DEMetro_Z_vs_SMC 0 4.193 0.000493 0.938
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.020 0.022 0.010 -0.215
SMC (0.0, 0.0) 0.021 0.022 0.010 -0.184
Metro (0.0, 0.0) 0.037 0.022 0.010 1.503
DEMetro_Z (0.0, 0.0) 0.045 0.022 0.010 2.375
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) 0.594 0.556 0.179
SMC (0.0, 0.0) -1.040 0.306 -0.291
Metro (0.0, 0.0) 2.921 0.00656 1.329
DEMetro_Z (0.0, 0.0) 3.988 0.00037 1.711
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.683 0.109 0.376
Metro_vs_DEMetro_Z 0 -0.800 0.434 -0.179
HMC_vs_Metro 0 -2.504 0.0215 -0.560
HMC_vs_DEMetro_Z 0 -3.150 0.00527 -0.704
Metro_vs_SMC 0 3.535 0.00221 0.790
DEMetro_Z_vs_SMC 0 5.032 7.41e-05 1.125
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.034 0.031 0.016 0.179
SMC (0.0, 0.0) 0.026 0.031 0.016 -0.291
Metro (0.0, 0.0) 0.052 0.031 0.016 1.329
DEMetro_Z (0.0, 0.0) 0.058 0.031 0.016 1.711
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) 0.045 0.964 0.016
SMC (0.0, 0.0) -0.318 0.753 -0.145
Metro (0.0, 0.0) 4.457 0.000174 3.083
DEMetro_Z (0.0, 0.0) 6.441 1.9e-06 5.618
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.565 0.0189 -0.574
DEMetro_Z_vs_SMC 0 6.420 3.73e-06 1.436
HMC_vs_DEMetro_Z 0 -7.432 4.92e-07 -1.662
HMC_vs_Metro 0 -4.319 0.00037 -0.966
HMC_vs_SMC 0 0.387 0.703 0.086
Metro_vs_SMC 0 4.600 0.000196 1.028
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.031 0.030 0.005 0.016
SMC (0.0, 0.0) 0.030 0.030 0.005 -0.145
Metro (0.0, 0.0) 0.045 0.030 0.005 3.083
DEMetro_Z (0.0, 0.0) 0.058 0.030 0.005 5.618
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0.0, 0.0) -0.086 0.932 -0.030
SMC (0.0, 0.0) -0.421 0.677 -0.166
Metro (0.0, 0.0) 4.135 0.000345 2.439
DEMetro_Z (0.0, 0.0) 5.346 1.93e-05 3.764
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.379 3.44e-05 1.203
HMC_vs_Metro 0 -4.003 0.00076 -0.895
Metro_vs_DEMetro_Z 0 -1.774 0.0921 -0.397
HMC_vs_SMC 0 0.339 0.739 0.076
Metro_vs_SMC 0 4.415 0.000298 0.987
HMC_vs_DEMetro_Z 0 -6.140 6.68e-06 -1.373
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0.0, 0.0) 0.015 0.015 0.004 -0.030
SMC (0.0, 0.0) 0.014 0.015 0.004 -0.166
Metro (0.0, 0.0) 0.024 0.015 0.004 2.439
DEMetro_Z (0.0, 0.0) 0.029 0.015 0.004 3.764
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
(0.0, 0.0) HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
(0.0, 0.0) HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
(0.0, 0.0)
Chain
(0.0, 0.0)

Correlation

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Vary_only_Correlation (MvNormal, correlation, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.052 0.959 0.016
HMC 0.3 1.300 0.202 0.375
HMC 0.5 1.884 0.0686 0.787
HMC 0.9 1.441 0.16 0.647
HMC 0.99 3.119 0.00398 1.415
SMC 0.0 -1.261 0.215 -0.403
SMC 0.3 0.560 0.579 0.162
SMC 0.5 0.190 0.85 0.072
SMC 0.9 -0.737 0.465 -0.244
SMC 0.99 -0.675 0.503 -0.215
Metro 0.0 3.790 0.000674 1.713
Metro 0.3 4.647 4.68e-05 1.759
Metro 0.5 3.126 0.00464 2.106
Metro 0.9 4.476 0.000221 5.254
Metro 0.99 4.343 0.000344 15.396
DEMetro_Z 0.0 2.900 0.00744 1.589
DEMetro_Z 0.3 3.060 0.00525 1.858
DEMetro_Z 0.5 4.325 0.000222 2.690
DEMetro_Z 0.9 2.984 0.00517 1.130
DEMetro_Z 0.99 1.966 0.0594 0.984
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -3.414 0.00291 -0.763
HMC_vs_DEMetro_Z 0.3 -2.534 0.0202 -0.567
HMC_vs_DEMetro_Z 0.5 -2.828 0.0107 -0.632
HMC_vs_DEMetro_Z 0.9 -0.889 0.385 -0.199
HMC_vs_DEMetro_Z 0.99 0.679 0.505 0.152
Metro_vs_SMC 0.0 4.735 0.000144 1.059
Metro_vs_SMC 0.3 4.414 0.000298 0.987
Metro_vs_SMC 0.5 2.707 0.014 0.605
Metro_vs_SMC 0.9 4.421 0.000293 0.989
Metro_vs_SMC 0.99 4.515 0.000237 1.010
Metro_vs_DEMetro_Z 0.0 0.219 0.829 0.049
Metro_vs_DEMetro_Z 0.3 -0.140 0.89 -0.031
Metro_vs_DEMetro_Z 0.5 -0.740 0.469 -0.165
Metro_vs_DEMetro_Z 0.9 3.097 0.00593 0.693
Metro_vs_DEMetro_Z 0.99 3.983 0.000797 0.891
HMC_vs_Metro 0.0 -4.067 0.000657 -0.909
HMC_vs_Metro 0.3 -4.947 8.94e-05 -1.106
HMC_vs_Metro 0.5 -1.778 0.0915 -0.397
HMC_vs_Metro 0.9 -4.033 0.00071 -0.902
HMC_vs_Metro 0.99 -4.050 0.000683 -0.906
HMC_vs_SMC 0.0 2.165 0.0433 0.484
HMC_vs_SMC 0.3 0.864 0.398 0.193
HMC_vs_SMC 0.5 2.009 0.0589 0.449
HMC_vs_SMC 0.9 1.904 0.0722 0.426
HMC_vs_SMC 0.99 3.769 0.0013 0.843
DEMetro_Z_vs_SMC 0.0 4.204 0.000481 0.940
DEMetro_Z_vs_SMC 0.3 2.861 0.01 0.640
DEMetro_Z_vs_SMC 0.5 4.370 0.000329 0.977
DEMetro_Z_vs_SMC 0.9 3.216 0.00455 0.719
DEMetro_Z_vs_SMC 0.99 2.174 0.0425 0.486
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.022 0.022 0.010 0.016
HMC 0.3 0.021 0.017 0.011 0.375
HMC 0.5 0.025 0.019 0.008 0.787
HMC 0.9 0.027 0.020 0.012 0.647
HMC 0.99 0.035 0.018 0.012 1.415
SMC 0.0 0.018 0.022 0.010 -0.403
SMC 0.3 0.019 0.017 0.011 0.162
SMC 0.5 0.019 0.019 0.008 0.072
SMC 0.9 0.017 0.020 0.012 -0.244
SMC 0.99 0.016 0.018 0.012 -0.215
Metro 0.0 0.039 0.022 0.010 1.713
Metro 0.3 0.037 0.017 0.011 1.759
Metro 0.5 0.035 0.019 0.008 2.106
Metro 0.9 0.081 0.020 0.012 5.254
Metro 0.99 0.202 0.018 0.012 15.396
DEMetro_Z 0.0 0.038 0.022 0.010 1.589
DEMetro_Z 0.3 0.038 0.017 0.011 1.858
DEMetro_Z 0.5 0.040 0.019 0.008 2.690
DEMetro_Z 0.9 0.033 0.020 0.012 1.130
DEMetro_Z 0.99 0.030 0.018 0.012 0.984
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.656 0.516 -0.191
HMC 0.3 0.575 0.569 0.191
HMC 0.5 0.565 0.575 0.198
HMC 0.9 1.772 0.0881 0.989
HMC 0.99 3.090 0.00436 1.452
SMC 0.0 -0.412 0.683 -0.137
SMC 0.3 0.666 0.509 0.208
SMC 0.5 1.094 0.282 0.432
SMC 0.9 -0.618 0.54 -0.212
SMC 0.99 0.409 0.685 0.164
Metro 0.0 1.504 0.141 0.550
Metro 0.3 3.339 0.00233 1.601
Metro 0.5 4.548 7.61e-05 1.951
Metro 0.9 3.619 0.0015 2.899
Metro 0.99 5.747 1.4e-05 11.476
DEMetro_Z 0.0 3.519 0.00116 1.202
DEMetro_Z 0.3 3.685 0.00104 2.008
DEMetro_Z 0.5 4.677 0.000108 3.508
DEMetro_Z 0.9 2.011 0.054 0.999
DEMetro_Z 0.99 2.201 0.0365 1.163
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -0.167 0.869 -0.037
HMC_vs_SMC 0.3 -0.054 0.958 -0.012
HMC_vs_SMC 0.5 -0.730 0.474 -0.163
HMC_vs_SMC 0.9 1.830 0.0829 0.409
HMC_vs_SMC 0.99 2.359 0.0292 0.528
Metro_vs_DEMetro_Z 0.0 -1.873 0.0765 -0.419
Metro_vs_DEMetro_Z 0.3 -0.532 0.601 -0.119
Metro_vs_DEMetro_Z 0.5 -1.713 0.103 -0.383
Metro_vs_DEMetro_Z 0.9 1.917 0.0703 0.429
Metro_vs_DEMetro_Z 0.99 4.769 0.000133 1.066
HMC_vs_Metro 0.0 -2.620 0.0168 -0.586
HMC_vs_Metro 0.3 -3.017 0.00709 -0.675
HMC_vs_Metro 0.5 -4.763 0.000135 -1.065
HMC_vs_Metro 0.9 -1.994 0.0607 -0.446
HMC_vs_Metro 0.99 -4.940 9.09e-05 -1.105
HMC_vs_DEMetro_Z 0.0 -4.439 0.000281 -0.993
HMC_vs_DEMetro_Z 0.3 -4.094 0.000618 -0.915
HMC_vs_DEMetro_Z 0.5 -4.833 0.000116 -1.081
HMC_vs_DEMetro_Z 0.9 -0.012 0.99 -0.003
HMC_vs_DEMetro_Z 0.99 0.482 0.635 0.108
Metro_vs_SMC 0.0 2.051 0.0543 0.459
Metro_vs_SMC 0.3 2.938 0.00844 0.657
Metro_vs_SMC 0.5 4.036 0.000706 0.902
Metro_vs_SMC 0.9 3.526 0.00226 0.788
Metro_vs_SMC 0.99 5.606 2.09e-05 1.253
DEMetro_Z_vs_SMC 0.0 3.180 0.00493 0.711
DEMetro_Z_vs_SMC 0.3 3.916 0.000929 0.876
DEMetro_Z_vs_SMC 0.5 3.969 0.000822 0.888
DEMetro_Z_vs_SMC 0.9 2.832 0.0106 0.633
DEMetro_Z_vs_SMC 0.99 1.597 0.127 0.357
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.028 0.031 0.016 -0.191
HMC 0.3 0.029 0.026 0.014 0.191
HMC 0.5 0.028 0.026 0.012 0.198
HMC 0.9 0.048 0.033 0.015 0.989
HMC 0.99 0.053 0.026 0.018 1.452
SMC 0.0 0.028 0.031 0.016 -0.137
SMC 0.3 0.029 0.026 0.014 0.208
SMC 0.5 0.031 0.026 0.012 0.432
SMC 0.9 0.029 0.033 0.015 -0.212
SMC 0.99 0.029 0.026 0.018 0.164
Metro 0.0 0.040 0.031 0.016 0.550
Metro 0.3 0.049 0.026 0.014 1.601
Metro 0.5 0.050 0.026 0.012 1.951
Metro 0.9 0.078 0.033 0.015 2.899
Metro 0.99 0.234 0.026 0.018 11.476
DEMetro_Z 0.0 0.050 0.031 0.016 1.202
DEMetro_Z 0.3 0.054 0.026 0.014 2.008
DEMetro_Z 0.5 0.069 0.026 0.012 3.508
DEMetro_Z 0.9 0.048 0.033 0.015 0.999
DEMetro_Z 0.99 0.047 0.026 0.018 1.163
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.326 0.746 0.112
HMC 0.3 1.153 0.256 0.357
HMC 0.5 2.001 0.0543 0.882
HMC 0.9 2.613 0.0141 1.245
HMC 0.99 5.161 1.46e-05 2.334
SMC 0.0 -1.656 0.107 -0.613
SMC 0.3 0.450 0.655 0.132
SMC 0.5 0.649 0.521 0.244
SMC 0.9 -0.055 0.956 -0.019
SMC 0.99 -0.267 0.791 -0.092
Metro 0.0 5.244 1.78e-05 2.946
Metro 0.3 6.565 2.16e-07 2.764
Metro 0.5 5.574 9.01e-06 3.450
Metro 0.9 5.599 1.73e-05 7.448
Metro 0.99 6.665 2.19e-06 28.081
DEMetro_Z 0.0 7.322 1.22e-07 4.489
DEMetro_Z 0.3 5.782 5.67e-06 3.702
DEMetro_Z 0.5 8.335 9.84e-09 4.857
DEMetro_Z 0.9 6.043 7.78e-07 2.377
DEMetro_Z 0.99 5.212 1.64e-05 2.676
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -2.297 0.0332 -0.514
Metro_vs_DEMetro_Z 0.3 -1.224 0.236 -0.274
Metro_vs_DEMetro_Z 0.5 -2.079 0.0514 -0.465
Metro_vs_DEMetro_Z 0.9 3.372 0.0032 0.754
Metro_vs_DEMetro_Z 0.99 5.970 9.58e-06 1.335
DEMetro_Z_vs_SMC 0.0 8.578 5.85e-08 1.918
DEMetro_Z_vs_SMC 0.3 6.060 7.91e-06 1.355
DEMetro_Z_vs_SMC 0.5 7.636 3.32e-07 1.708
DEMetro_Z_vs_SMC 0.9 5.535 2.44e-05 1.238
DEMetro_Z_vs_SMC 0.99 4.396 0.000311 0.983
HMC_vs_DEMetro_Z 0.0 -6.836 1.59e-06 -1.529
HMC_vs_DEMetro_Z 0.3 -5.670 1.82e-05 -1.268
HMC_vs_DEMetro_Z 0.5 -5.695 1.72e-05 -1.274
HMC_vs_DEMetro_Z 0.9 -2.033 0.0563 -0.455
HMC_vs_DEMetro_Z 0.99 -0.550 0.589 -0.123
HMC_vs_Metro 0.0 -5.312 3.98e-05 -1.188
HMC_vs_Metro 0.3 -6.311 4.67e-06 -1.411
HMC_vs_Metro 0.5 -3.630 0.00178 -0.812
HMC_vs_Metro 0.9 -5.137 5.86e-05 -1.149
HMC_vs_Metro 0.99 -6.216 5.69e-06 -1.390
HMC_vs_SMC 0.0 2.218 0.0389 0.496
HMC_vs_SMC 0.3 0.768 0.452 0.172
HMC_vs_SMC 0.5 1.656 0.114 0.370
HMC_vs_SMC 0.9 2.215 0.0392 0.495
HMC_vs_SMC 0.99 4.625 0.000185 1.034
Metro_vs_SMC 0.0 6.041 8.23e-06 1.351
Metro_vs_SMC 0.3 6.348 4.32e-06 1.420
Metro_vs_SMC 0.5 4.633 0.000181 1.036
Metro_vs_SMC 0.9 5.450 2.94e-05 1.219
Metro_vs_SMC 0.99 6.715 2.03e-06 1.502
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.031 0.030 0.005 0.112
HMC 0.3 0.029 0.027 0.007 0.357
HMC 0.5 0.033 0.028 0.006 0.882
HMC 0.9 0.037 0.028 0.008 1.245
HMC 0.99 0.043 0.025 0.008 2.334
SMC 0.0 0.028 0.030 0.005 -0.613
SMC 0.3 0.028 0.027 0.007 0.132
SMC 0.5 0.029 0.028 0.006 0.244
SMC 0.9 0.028 0.028 0.008 -0.019
SMC 0.99 0.025 0.025 0.008 -0.092
Metro 0.0 0.045 0.030 0.005 2.946
Metro 0.3 0.045 0.027 0.007 2.764
Metro 0.5 0.047 0.028 0.006 3.450
Metro 0.9 0.084 0.028 0.008 7.448
Metro 0.99 0.241 0.025 0.008 28.081
DEMetro_Z 0.0 0.052 0.030 0.005 4.489
DEMetro_Z 0.3 0.051 0.027 0.007 3.702
DEMetro_Z 0.5 0.055 0.028 0.006 4.857
DEMetro_Z 0.9 0.046 0.028 0.008 2.377
DEMetro_Z 0.99 0.046 0.025 0.008 2.676
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.238 0.813 -0.069
HMC 0.3 0.741 0.464 0.241
HMC 0.5 2.112 0.042 0.820
HMC 0.9 2.114 0.0419 0.827
HMC 0.99 4.877 2.13e-05 1.732
SMC 0.0 -1.369 0.18 -0.515
SMC 0.3 0.377 0.708 0.113
SMC 0.5 0.544 0.59 0.192
SMC 0.9 -0.021 0.983 -0.006
SMC 0.99 -0.951 0.348 -0.329
Metro 0.0 4.366 0.000167 2.289
Metro 0.3 5.825 1.65e-06 2.373
Metro 0.5 5.139 2.2e-05 2.776
Metro 0.9 5.472 1.91e-05 5.185
Metro 0.99 8.357 7.89e-08 23.029
DEMetro_Z 0.0 5.719 4.12e-06 2.913
DEMetro_Z 0.3 4.359 0.000199 2.648
DEMetro_Z 0.5 7.399 5.46e-08 3.827
DEMetro_Z 0.9 4.727 3.74e-05 1.804
DEMetro_Z 0.99 3.570 0.00129 1.727
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 6.855 1.53e-06 1.533
DEMetro_Z_vs_SMC 0.3 4.705 0.000154 1.052
DEMetro_Z_vs_SMC 0.5 6.694 2.12e-06 1.497
DEMetro_Z_vs_SMC 0.9 4.873 0.000106 1.090
DEMetro_Z_vs_SMC 0.99 3.498 0.00241 0.782
HMC_vs_Metro 0.0 -5.759 1.5e-05 -1.288
HMC_vs_Metro 0.3 -5.400 3.28e-05 -1.207
HMC_vs_Metro 0.5 -3.552 0.00213 -0.794
HMC_vs_Metro 0.9 -4.630 0.000183 -1.035
HMC_vs_Metro 0.99 -7.817 2.36e-07 -1.748
Metro_vs_DEMetro_Z 0.0 -0.954 0.352 -0.213
Metro_vs_DEMetro_Z 0.3 -0.379 0.709 -0.085
Metro_vs_DEMetro_Z 0.5 -1.766 0.0935 -0.395
Metro_vs_DEMetro_Z 0.9 3.105 0.00583 0.694
Metro_vs_DEMetro_Z 0.99 7.727 2.8e-07 1.728
HMC_vs_SMC 0.0 1.309 0.206 0.293
HMC_vs_SMC 0.3 0.449 0.658 0.101
HMC_vs_SMC 0.5 2.051 0.0543 0.459
HMC_vs_SMC 0.9 1.796 0.0884 0.402
HMC_vs_SMC 0.99 4.820 0.000119 1.078
Metro_vs_SMC 0.0 4.988 8.17e-05 1.115
Metro_vs_SMC 0.3 5.561 2.31e-05 1.243
Metro_vs_SMC 0.5 4.338 0.000354 0.970
Metro_vs_SMC 0.9 5.392 3.34e-05 1.206
Metro_vs_SMC 0.99 8.426 7.69e-08 1.884
HMC_vs_DEMetro_Z 0.0 -6.192 5.99e-06 -1.385
HMC_vs_DEMetro_Z 0.3 -4.302 0.000384 -0.962
HMC_vs_DEMetro_Z 0.5 -5.227 4.8e-05 -1.169
HMC_vs_DEMetro_Z 0.9 -2.263 0.0355 -0.506
HMC_vs_DEMetro_Z 0.99 0.009 0.993 0.002
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.014 0.015 0.004 -0.069
HMC 0.3 0.014 0.013 0.005 0.241
HMC 0.5 0.017 0.014 0.004 0.820
HMC 0.9 0.020 0.015 0.006 0.827
HMC 0.99 0.023 0.014 0.005 1.732
SMC 0.0 0.013 0.015 0.004 -0.515
SMC 0.3 0.013 0.013 0.005 0.113
SMC 0.5 0.014 0.014 0.004 0.192
SMC 0.9 0.015 0.015 0.006 -0.006
SMC 0.99 0.013 0.014 0.005 -0.329
Metro 0.0 0.023 0.015 0.004 2.289
Metro 0.3 0.024 0.013 0.005 2.373
Metro 0.5 0.025 0.014 0.004 2.776
Metro 0.9 0.046 0.015 0.006 5.185
Metro 0.99 0.134 0.014 0.005 23.029
DEMetro_Z 0.0 0.025 0.015 0.004 2.913
DEMetro_Z 0.3 0.025 0.013 0.005 2.648
DEMetro_Z 0.5 0.029 0.014 0.004 3.827
DEMetro_Z 0.9 0.026 0.015 0.006 1.804
DEMetro_Z 0.99 0.023 0.014 0.005 1.727
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.294 0.771 0.106
HMC 0.3 1.153 0.256 0.407
HMC 0.5 1.440 0.16 0.639
HMC 0.9 1.459 0.153 0.534
HMC 0.99 2.800 0.00932 1.464
SMC 0.0 -0.814 0.421 -0.263
SMC 0.3 -0.012 0.99 -0.004
SMC 0.5 0.271 0.788 0.095
SMC 0.9 -1.118 0.271 -0.376
SMC 0.99 -3.410 0.00197 -0.857
Metro 0.0 2.098 0.0436 0.843
Metro 0.3 3.021 0.00583 1.885
Metro 0.5 3.482 0.00224 3.565
Metro 0.9 4.878 9.29e-05 7.367
Metro 0.99 7.079 9.59e-07 35.204
DEMetro_Z 0.0 3.077 0.00502 1.844
DEMetro_Z 0.3 4.520 7.2e-05 1.773
DEMetro_Z 0.5 3.676 0.00124 2.606
DEMetro_Z 0.9 2.541 0.0174 1.435
DEMetro_Z 0.99 1.887 0.0719 1.360
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -3.094 0.00597 -0.692
HMC_vs_DEMetro_Z 0.3 -3.588 0.00196 -0.802
HMC_vs_DEMetro_Z 0.5 -2.536 0.0201 -0.567
HMC_vs_DEMetro_Z 0.9 -1.584 0.13 -0.354
HMC_vs_DEMetro_Z 0.99 0.127 0.9 0.028
Metro_vs_SMC 0.0 3.491 0.00244 0.781
Metro_vs_SMC 0.3 3.046 0.00664 0.681
Metro_vs_SMC 0.5 3.211 0.0046 0.718
Metro_vs_SMC 0.9 4.930 9.29e-05 1.102
Metro_vs_SMC 0.99 7.252 6.98e-07 1.622
Metro_vs_DEMetro_Z 0.0 -1.505 0.149 -0.336
Metro_vs_DEMetro_Z 0.3 0.183 0.857 0.041
Metro_vs_DEMetro_Z 0.5 0.706 0.489 0.158
Metro_vs_DEMetro_Z 0.9 3.436 0.00277 0.768
Metro_vs_DEMetro_Z 0.99 6.436 3.6e-06 1.439
HMC_vs_Metro 0.0 -1.847 0.0804 -0.413
HMC_vs_Metro 0.3 -2.530 0.0204 -0.566
HMC_vs_Metro 0.5 -2.533 0.0203 -0.566
HMC_vs_Metro 0.9 -4.547 0.00022 -1.017
HMC_vs_Metro 0.99 -7.048 1.04e-06 -1.576
HMC_vs_SMC 0.0 1.458 0.161 0.326
HMC_vs_SMC 0.3 1.523 0.144 0.340
HMC_vs_SMC 0.5 1.379 0.184 0.308
HMC_vs_SMC 0.9 2.272 0.0349 0.508
HMC_vs_SMC 0.99 4.575 0.000207 1.023
DEMetro_Z_vs_SMC 0.0 3.351 0.00335 0.749
DEMetro_Z_vs_SMC 0.3 4.628 0.000184 1.035
DEMetro_Z_vs_SMC 0.5 3.633 0.00177 0.812
DEMetro_Z_vs_SMC 0.9 2.817 0.011 0.630
DEMetro_Z_vs_SMC 0.99 3.054 0.00653 0.683
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.023 0.022 0.010 0.106
HMC 0.3 0.022 0.017 0.011 0.407
HMC 0.5 0.024 0.019 0.008 0.639
HMC 0.9 0.026 0.020 0.012 0.534
HMC 0.99 0.036 0.018 0.012 1.464
SMC 0.0 0.020 0.022 0.010 -0.263
SMC 0.3 0.017 0.017 0.011 -0.004
SMC 0.5 0.019 0.019 0.008 0.095
SMC 0.9 0.015 0.020 0.012 -0.376
SMC 0.99 0.008 0.018 0.012 -0.857
Metro 0.0 0.030 0.022 0.010 0.843
Metro 0.3 0.038 0.017 0.011 1.885
Metro 0.5 0.047 0.019 0.008 3.565
Metro 0.9 0.106 0.020 0.012 7.367
Metro 0.99 0.437 0.018 0.012 35.204
DEMetro_Z 0.0 0.040 0.022 0.010 1.844
DEMetro_Z 0.3 0.037 0.017 0.011 1.773
DEMetro_Z 0.5 0.039 0.019 0.008 2.606
DEMetro_Z 0.9 0.037 0.020 0.012 1.435
DEMetro_Z 0.99 0.035 0.018 0.012 1.360
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.106 0.916 -0.033
HMC 0.3 1.970 0.0568 0.744
HMC 0.5 0.511 0.612 0.185
HMC 0.9 1.548 0.133 0.775
HMC 0.99 1.937 0.0621 0.859
SMC 0.0 -0.846 0.403 -0.241
SMC 0.3 -0.190 0.851 -0.062
SMC 0.5 0.486 0.63 0.173
SMC 0.9 0.922 0.363 0.316
SMC 0.99 0.658 0.515 0.263
Metro 0.0 3.471 0.00132 1.165
Metro 0.3 3.667 0.000803 1.366
Metro 0.5 3.534 0.00133 1.576
Metro 0.9 4.589 0.00015 4.094
Metro 0.99 4.506 0.000236 13.144
DEMetro_Z 0.0 3.526 0.00147 1.748
DEMetro_Z 0.3 4.635 6.45e-05 2.095
DEMetro_Z 0.5 4.484 0.000117 2.282
DEMetro_Z 0.9 2.819 0.00957 1.887
DEMetro_Z 0.99 2.164 0.0375 0.827
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 0.666 0.513 0.149
HMC_vs_SMC 0.3 2.261 0.0357 0.506
HMC_vs_SMC 0.5 0.064 0.95 0.014
HMC_vs_SMC 0.9 0.955 0.352 0.213
HMC_vs_SMC 0.99 1.034 0.314 0.231
Metro_vs_DEMetro_Z 0.0 -1.136 0.27 -0.254
Metro_vs_DEMetro_Z 0.3 -1.526 0.144 -0.341
Metro_vs_DEMetro_Z 0.5 -1.337 0.197 -0.299
Metro_vs_DEMetro_Z 0.9 2.200 0.0404 0.492
Metro_vs_DEMetro_Z 0.99 4.568 0.00021 1.021
HMC_vs_Metro 0.0 -3.754 0.00134 -0.839
HMC_vs_Metro 0.3 -1.599 0.126 -0.357
HMC_vs_Metro 0.5 -2.485 0.0224 -0.556
HMC_vs_Metro 0.9 -3.185 0.00488 -0.712
HMC_vs_Metro 0.99 -4.120 0.000583 -0.921
HMC_vs_DEMetro_Z 0.0 -3.272 0.00401 -0.732
HMC_vs_DEMetro_Z 0.3 -2.524 0.0207 -0.564
HMC_vs_DEMetro_Z 0.5 -4.277 0.000407 -0.956
HMC_vs_DEMetro_Z 0.9 -1.485 0.154 -0.332
HMC_vs_DEMetro_Z 0.99 0.067 0.947 0.015
Metro_vs_SMC 0.0 4.315 0.000373 0.965
Metro_vs_SMC 0.3 4.154 0.00054 0.929
Metro_vs_SMC 0.5 2.463 0.0235 0.551
Metro_vs_SMC 0.9 4.027 0.000721 0.900
Metro_vs_SMC 0.99 4.647 0.000176 1.039
DEMetro_Z_vs_SMC 0.0 3.980 0.000802 0.890
DEMetro_Z_vs_SMC 0.3 4.410 0.000301 0.986
DEMetro_Z_vs_SMC 0.5 4.117 0.000587 0.921
DEMetro_Z_vs_SMC 0.9 2.117 0.0477 0.473
DEMetro_Z_vs_SMC 0.99 1.626 0.12 0.364
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.030 0.031 0.016 -0.033
HMC 0.3 0.036 0.026 0.014 0.744
HMC 0.5 0.028 0.026 0.012 0.185
HMC 0.9 0.045 0.033 0.015 0.775
HMC 0.99 0.042 0.026 0.018 0.859
SMC 0.0 0.027 0.031 0.016 -0.241
SMC 0.3 0.025 0.026 0.014 -0.062
SMC 0.5 0.028 0.026 0.012 0.173
SMC 0.9 0.038 0.033 0.015 0.316
SMC 0.99 0.031 0.026 0.018 0.263
Metro 0.0 0.049 0.031 0.016 1.165
Metro 0.3 0.045 0.026 0.014 1.366
Metro 0.5 0.045 0.026 0.012 1.576
Metro 0.9 0.096 0.033 0.015 4.094
Metro 0.99 0.264 0.026 0.018 13.144
DEMetro_Z 0.0 0.059 0.031 0.016 1.748
DEMetro_Z 0.3 0.056 0.026 0.014 2.095
DEMetro_Z 0.5 0.054 0.026 0.012 2.282
DEMetro_Z 0.9 0.062 0.033 0.015 1.887
DEMetro_Z 0.99 0.041 0.026 0.018 0.827
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.102 0.919 0.040
HMC 0.3 2.473 0.0183 0.907
HMC 0.5 1.945 0.0599 0.736
HMC 0.9 2.462 0.019 0.948
HMC 0.99 3.593 0.00139 2.127
SMC 0.0 -1.475 0.15 -0.599
SMC 0.3 0.567 0.574 0.183
SMC 0.5 0.993 0.327 0.302
SMC 0.9 0.402 0.69 0.138
SMC 0.99 -0.994 0.327 -0.289
Metro 0.0 3.991 0.000437 2.019
Metro 0.3 3.928 0.000696 3.033
Metro 0.5 3.958 0.000753 4.760
Metro 0.9 6.505 2.6e-06 10.601
Metro 0.99 8.149 1.25e-07 50.693
DEMetro_Z 0.0 5.950 5.39e-06 4.835
DEMetro_Z 0.3 8.706 6.23e-10 3.676
DEMetro_Z 0.5 6.305 1.65e-06 4.142
DEMetro_Z 0.9 5.293 1.65e-05 3.059
DEMetro_Z 0.99 4.672 0.000106 3.397
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -2.982 0.00766 -0.667
Metro_vs_DEMetro_Z 0.3 -0.827 0.419 -0.185
Metro_vs_DEMetro_Z 0.5 0.435 0.668 0.097
Metro_vs_DEMetro_Z 0.9 3.980 0.000803 0.890
Metro_vs_DEMetro_Z 0.99 7.253 6.96e-07 1.622
DEMetro_Z_vs_SMC 0.0 5.988 9.22e-06 1.339
DEMetro_Z_vs_SMC 0.3 8.640 5.24e-08 1.932
DEMetro_Z_vs_SMC 0.5 6.452 3.49e-06 1.443
DEMetro_Z_vs_SMC 0.9 4.705 0.000154 1.052
DEMetro_Z_vs_SMC 0.99 4.986 8.21e-05 1.115
HMC_vs_DEMetro_Z 0.0 -6.084 7.51e-06 -1.361
HMC_vs_DEMetro_Z 0.3 -6.175 6.2e-06 -1.381
HMC_vs_DEMetro_Z 0.5 -4.815 0.00012 -1.077
HMC_vs_DEMetro_Z 0.9 -3.361 0.00328 -0.752
HMC_vs_DEMetro_Z 0.99 -1.377 0.184 -0.308
HMC_vs_Metro 0.0 -3.979 0.000804 -0.890
HMC_vs_Metro 0.3 -3.137 0.00542 -0.702
HMC_vs_Metro 0.5 -3.298 0.00379 -0.737
HMC_vs_Metro 0.9 -6.118 6.99e-06 -1.368
HMC_vs_Metro 0.99 -8.052 1.52e-07 -1.801
HMC_vs_SMC 0.0 1.514 0.147 0.339
HMC_vs_SMC 0.3 2.116 0.0478 0.473
HMC_vs_SMC 0.5 1.493 0.152 0.334
HMC_vs_SMC 0.9 1.977 0.0628 0.442
HMC_vs_SMC 0.99 4.176 0.000513 0.934
Metro_vs_SMC 0.0 5.071 6.78e-05 1.134
Metro_vs_SMC 0.3 3.613 0.00185 0.808
Metro_vs_SMC 0.5 3.716 0.00147 0.831
Metro_vs_SMC 0.9 6.158 6.42e-06 1.377
Metro_vs_SMC 0.99 8.251 1.06e-07 1.845
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.031 0.030 0.005 0.040
HMC 0.3 0.033 0.027 0.007 0.907
HMC 0.5 0.032 0.028 0.006 0.736
HMC 0.9 0.035 0.028 0.008 0.948
HMC 0.99 0.042 0.025 0.008 2.127
SMC 0.0 0.028 0.030 0.005 -0.599
SMC 0.3 0.028 0.027 0.007 0.183
SMC 0.5 0.029 0.028 0.006 0.302
SMC 0.9 0.029 0.028 0.008 0.138
SMC 0.99 0.023 0.025 0.008 -0.289
Metro 0.0 0.040 0.030 0.005 2.019
Metro 0.3 0.047 0.027 0.007 3.033
Metro 0.5 0.054 0.028 0.006 4.760
Metro 0.9 0.108 0.028 0.008 10.601
Metro 0.99 0.415 0.025 0.008 50.693
DEMetro_Z 0.0 0.054 0.030 0.005 4.835
DEMetro_Z 0.3 0.051 0.027 0.007 3.676
DEMetro_Z 0.5 0.051 0.028 0.006 4.142
DEMetro_Z 0.9 0.051 0.028 0.008 3.059
DEMetro_Z 0.99 0.051 0.025 0.008 3.397
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.354 0.725 0.129
HMC 0.3 2.351 0.0243 0.838
HMC 0.5 1.779 0.0839 0.664
HMC 0.9 2.189 0.0349 0.683
HMC 0.99 3.344 0.00233 1.641
SMC 0.0 -1.439 0.159 -0.506
SMC 0.3 0.559 0.58 0.189
SMC 0.5 1.484 0.146 0.467
SMC 0.9 0.884 0.382 0.282
SMC 0.99 -1.089 0.283 -0.344
Metro 0.0 2.744 0.00988 1.162
Metro 0.3 3.391 0.00246 2.310
Metro 0.5 4.311 0.000277 3.441
Metro 0.9 6.521 2.09e-06 7.548
Metro 0.99 8.419 7.54e-08 41.070
DEMetro_Z 0.0 4.974 4.54e-05 3.295
DEMetro_Z 0.3 6.851 8.65e-08 2.817
DEMetro_Z 0.5 4.661 9.56e-05 2.955
DEMetro_Z 0.9 3.871 0.000656 2.169
DEMetro_Z 0.99 3.820 0.000872 2.716
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 5.133 5.92e-05 1.148
DEMetro_Z_vs_SMC 0.3 6.475 3.32e-06 1.448
DEMetro_Z_vs_SMC 0.5 4.469 0.000263 0.999
DEMetro_Z_vs_SMC 0.9 3.527 0.00225 0.789
DEMetro_Z_vs_SMC 0.99 4.214 0.00047 0.942
HMC_vs_Metro 0.0 -2.413 0.0261 -0.540
HMC_vs_Metro 0.3 -2.739 0.013 -0.612
HMC_vs_Metro 0.5 -3.240 0.00431 -0.724
HMC_vs_Metro 0.9 -6.371 4.12e-06 -1.425
HMC_vs_Metro 0.99 -8.307 9.54e-08 -1.857
Metro_vs_DEMetro_Z 0.0 -2.807 0.0113 -0.628
Metro_vs_DEMetro_Z 0.3 -0.717 0.482 -0.160
Metro_vs_DEMetro_Z 0.5 0.444 0.662 0.099
Metro_vs_DEMetro_Z 0.9 3.832 0.00112 0.857
Metro_vs_DEMetro_Z 0.99 7.515 4.19e-07 1.680
HMC_vs_SMC 0.0 1.730 0.0999 0.387
HMC_vs_SMC 0.3 1.970 0.0636 0.440
HMC_vs_SMC 0.5 0.742 0.467 0.166
HMC_vs_SMC 0.9 1.376 0.185 0.308
HMC_vs_SMC 0.99 3.639 0.00175 0.814
Metro_vs_SMC 0.0 3.852 0.00108 0.861
Metro_vs_SMC 0.3 3.065 0.00637 0.685
Metro_vs_SMC 0.5 3.569 0.00205 0.798
Metro_vs_SMC 0.9 6.211 5.76e-06 1.389
Metro_vs_SMC 0.99 8.543 6.23e-08 1.910
HMC_vs_DEMetro_Z 0.0 -4.658 0.000171 -1.042
HMC_vs_DEMetro_Z 0.3 -4.705 0.000154 -1.052
HMC_vs_DEMetro_Z 0.5 -3.626 0.0018 -0.811
HMC_vs_DEMetro_Z 0.9 -2.706 0.014 -0.605
HMC_vs_DEMetro_Z 0.99 -1.312 0.205 -0.293
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.015 0.015 0.004 0.129
HMC 0.3 0.017 0.013 0.005 0.838
HMC 0.5 0.016 0.014 0.004 0.664
HMC 0.9 0.019 0.015 0.006 0.683
HMC 0.99 0.023 0.014 0.005 1.641
SMC 0.0 0.013 0.015 0.004 -0.506
SMC 0.3 0.014 0.013 0.005 0.189
SMC 0.5 0.015 0.014 0.004 0.467
SMC 0.9 0.017 0.015 0.006 0.282
SMC 0.99 0.013 0.014 0.005 -0.344
Metro 0.0 0.019 0.015 0.004 1.162
Metro 0.3 0.024 0.013 0.005 2.310
Metro 0.5 0.028 0.014 0.004 3.441
Metro 0.9 0.060 0.015 0.006 7.548
Metro 0.99 0.228 0.014 0.005 41.070
DEMetro_Z 0.0 0.027 0.015 0.004 3.295
DEMetro_Z 0.3 0.026 0.013 0.005 2.817
DEMetro_Z 0.5 0.026 0.014 0.004 2.955
DEMetro_Z 0.9 0.028 0.015 0.006 2.169
DEMetro_Z 0.99 0.028 0.014 0.005 2.716
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_high_Dimension (MvNormal, correlation, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -4.882 3.26e-05 -1.253
HMC 0.3 2.023 0.0556 1.774
HMC 0.5 2.116 0.0428 0.961
HMC 0.9 6.107 5.88e-06 9.088
HMC 0.99 4.030 0.000648 5.235
SMC 0.0 0.425 0.673 0.171
SMC 0.3 1.908 0.0658 0.842
SMC 0.5 -0.725 0.473 -0.200
SMC 0.9 -0.657 0.515 -0.231
SMC 0.99 0.244 0.809 0.071
Metro 0.0 14.400 5.39e-16 5.650
Metro 0.3 4.654 0.000169 15.657
Metro 0.5 5.218 4.63e-05 12.304
Metro 0.9 5.626 1.98e-05 32.631
Metro 0.99 4.250 0.000432 40.269
DEMetro_Z 0.0 29.309 2.79e-17 2283.554
DEMetro_Z 0.3 39.444 1.08e-19 2298.573
DEMetro_Z 0.5 38.616 1.6e-19 934.866
DEMetro_Z 0.9 43.423 1.75e-20 668.764
DEMetro_Z 0.99 29.121 3.09e-17 341.717
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -29.327 2.76e-17 -6.558
HMC_vs_DEMetro_Z 0.3 -39.454 1.08e-19 -8.822
HMC_vs_DEMetro_Z 0.5 -38.852 1.44e-19 -8.687
HMC_vs_DEMetro_Z 0.9 -42.736 2.39e-20 -9.556
HMC_vs_DEMetro_Z 0.99 -29.713 2.16e-17 -6.644
Metro_vs_SMC 0.0 12.856 8.02e-11 2.875
Metro_vs_SMC 0.3 4.506 0.000242 1.008
Metro_vs_SMC 0.5 5.213 4.96e-05 1.166
Metro_vs_SMC 0.9 5.627 2e-05 1.258
Metro_vs_SMC 0.99 4.242 0.000441 0.948
Metro_vs_DEMetro_Z 0.0 -29.237 2.92e-17 -6.538
Metro_vs_DEMetro_Z 0.3 -38.898 1.4e-19 -8.698
Metro_vs_DEMetro_Z 0.5 -37.882 2.31e-19 -8.471
Metro_vs_DEMetro_Z 0.9 -33.063 2.95e-18 -7.393
Metro_vs_DEMetro_Z 0.99 -17.384 4e-13 -3.887
HMC_vs_Metro 0.0 -19.482 5.13e-14 -4.356
HMC_vs_Metro 0.3 -4.276 0.000408 -0.956
HMC_vs_Metro 0.5 -4.614 0.000189 -1.032
HMC_vs_Metro 0.9 -3.634 0.00177 -0.813
HMC_vs_Metro 0.99 -3.562 0.00208 -0.796
HMC_vs_SMC 0.0 -4.331 0.00036 -0.968
HMC_vs_SMC 0.3 1.230 0.234 0.275
HMC_vs_SMC 0.5 2.972 0.00784 0.664
HMC_vs_SMC 0.9 6.528 2.98e-06 1.460
HMC_vs_SMC 0.99 3.825 0.00114 0.855
DEMetro_Z_vs_SMC 0.0 29.289 2.83e-17 6.549
DEMetro_Z_vs_SMC 0.3 39.507 1.05e-19 8.834
DEMetro_Z_vs_SMC 0.5 38.726 1.53e-19 8.659
DEMetro_Z_vs_SMC 0.9 43.532 1.69e-20 9.734
DEMetro_Z_vs_SMC 0.99 28.956 3.5e-17 6.475
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.019 0.023 0.003 -1.253
HMC 0.3 0.026 0.021 0.003 1.774
HMC 0.5 0.029 0.022 0.008 0.961
HMC 0.9 0.110 0.020 0.010 9.088
HMC 0.99 0.110 0.020 0.017 5.235
SMC 0.0 0.023 0.023 0.003 0.171
SMC 0.3 0.024 0.021 0.003 0.842
SMC 0.5 0.020 0.022 0.008 -0.200
SMC 0.9 0.018 0.020 0.010 -0.231
SMC 0.99 0.022 0.020 0.017 0.071
Metro 0.0 0.039 0.023 0.003 5.650
Metro 0.3 0.068 0.021 0.003 15.657
Metro 0.5 0.115 0.022 0.008 12.304
Metro 0.9 0.343 0.020 0.010 32.631
Metro 0.99 0.713 0.020 0.017 40.269
DEMetro_Z 0.0 6.514 0.023 0.003 2283.554
DEMetro_Z 0.3 6.831 0.021 0.003 2298.573
DEMetro_Z 0.5 7.144 0.022 0.008 934.866
DEMetro_Z 0.9 6.644 0.020 0.010 668.764
DEMetro_Z 0.99 5.901 0.020 0.017 341.717
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 7.544 1.03e-08 3.005
HMC 0.3 1.676 0.103 0.640
HMC 0.5 3.019 0.00541 1.532
HMC 0.9 4.214 0.000436 6.767
HMC 0.99 3.099 0.00581 7.364
SMC 0.0 2.857 0.0069 0.877
SMC 0.3 1.048 0.303 0.452
SMC 0.5 0.792 0.433 0.269
SMC 0.9 0.851 0.4 0.279
SMC 0.99 -0.399 0.693 -0.112
Metro 0.0 10.105 3.59e-11 4.595
Metro 0.3 7.305 2.81e-07 6.335
Metro 0.5 5.187 4.44e-05 7.040
Metro 0.9 8.120 1.23e-07 23.458
Metro 0.99 4.439 0.000282 140.313
DEMetro_Z 0.0 25.975 2.63e-16 40537.036
DEMetro_Z 0.3 34.801 1.13e-18 44793.345
DEMetro_Z 0.5 29.068 3.26e-17 22986.462
DEMetro_Z 0.9 37.102 3.41e-19 13666.123
DEMetro_Z 0.99 35.347 8.45e-19 10192.793
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 6.814 1.67e-06 1.524
HMC_vs_SMC 0.3 0.407 0.689 0.091
HMC_vs_SMC 0.5 2.336 0.0306 0.522
HMC_vs_SMC 0.9 4.061 0.000666 0.908
HMC_vs_SMC 0.99 3.113 0.00572 0.696
Metro_vs_DEMetro_Z 0.0 -25.974 2.63e-16 -5.808
Metro_vs_DEMetro_Z 0.3 -34.781 1.14e-18 -7.777
Metro_vs_DEMetro_Z 0.5 -29.050 3.29e-17 -6.496
Metro_vs_DEMetro_Z 0.9 -36.994 3.6e-19 -8.272
Metro_vs_DEMetro_Z 0.99 -33.533 2.27e-18 -7.498
HMC_vs_Metro 0.0 -2.630 0.0165 -0.588
HMC_vs_Metro 0.3 -6.165 6.34e-06 -1.378
HMC_vs_Metro 0.5 -3.887 0.000993 -0.869
HMC_vs_Metro 0.9 -4.982 8.27e-05 -1.114
HMC_vs_Metro 0.99 -4.389 0.000315 -0.981
HMC_vs_DEMetro_Z 0.0 -25.973 2.63e-16 -5.808
HMC_vs_DEMetro_Z 0.3 -34.802 1.13e-18 -7.782
HMC_vs_DEMetro_Z 0.5 -29.067 3.26e-17 -6.499
HMC_vs_DEMetro_Z 0.9 -37.029 3.54e-19 -8.280
HMC_vs_DEMetro_Z 0.99 -35.203 9.13e-19 -7.872
Metro_vs_SMC 0.0 9.132 2.22e-08 2.042
Metro_vs_SMC 0.3 6.400 3.88e-06 1.431
Metro_vs_SMC 0.5 4.758 0.000137 1.064
Metro_vs_SMC 0.9 7.889 2.06e-07 1.764
Metro_vs_SMC 0.99 4.432 0.000286 0.991
DEMetro_Z_vs_SMC 0.0 25.975 2.63e-16 5.808
DEMetro_Z_vs_SMC 0.3 34.802 1.13e-18 7.782
DEMetro_Z_vs_SMC 0.5 29.067 3.26e-17 6.499
DEMetro_Z_vs_SMC 0.9 37.095 3.42e-19 8.295
DEMetro_Z_vs_SMC 0.99 35.354 8.42e-19 7.905
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.044 0.032 0.004 3.005
HMC 0.3 0.035 0.032 0.004 0.640
HMC 0.5 0.043 0.031 0.008 1.532
HMC 0.9 0.108 0.024 0.012 6.767
HMC 0.99 0.133 0.026 0.015 7.364
SMC 0.0 0.035 0.032 0.004 0.877
SMC 0.3 0.034 0.032 0.004 0.452
SMC 0.5 0.033 0.031 0.008 0.269
SMC 0.9 0.028 0.024 0.012 0.279
SMC 0.99 0.024 0.026 0.015 -0.112
Metro 0.0 0.050 0.032 0.004 4.595
Metro 0.3 0.059 0.032 0.004 6.335
Metro 0.5 0.087 0.031 0.008 7.040
Metro 0.9 0.315 0.024 0.012 23.458
Metro 0.99 2.081 0.026 0.015 140.313
DEMetro_Z 0.0 162.043 0.032 0.004 40537.036
DEMetro_Z 0.3 185.874 0.032 0.004 44793.345
DEMetro_Z 0.5 180.854 0.031 0.008 22986.462
DEMetro_Z 0.9 169.617 0.024 0.012 13666.123
DEMetro_Z 0.99 149.359 0.026 0.015 10192.793
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.370 0.714 -0.095
HMC 0.3 2.799 0.0107 2.585
HMC 0.5 3.150 0.00379 1.518
HMC 0.9 7.009 9.81e-07 14.088
HMC 0.99 7.436 3.3e-07 9.426
SMC 0.0 1.284 0.208 0.525
SMC 0.3 2.273 0.0305 1.072
SMC 0.5 -0.495 0.624 -0.126
SMC 0.9 -0.525 0.603 -0.194
SMC 0.99 -0.348 0.73 -0.101
Metro 0.0 16.265 6.17e-17 6.912
Metro 0.3 5.186 5.16e-05 21.500
Metro 0.5 5.627 1.91e-05 16.468
Metro 0.9 7.244 7.01e-07 51.614
Metro 0.99 7.082 9.71e-07 80.330
DEMetro_Z 0.0 47.774 2.94e-21 5926.234
DEMetro_Z 0.3 75.569 5.05e-25 6357.251
DEMetro_Z 0.5 69.400 2.52e-24 2342.786
DEMetro_Z 0.9 80.444 1.53e-25 1850.420
DEMetro_Z 0.99 61.495 2.45e-23 890.174
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -47.734 2.98e-21 -10.674
Metro_vs_DEMetro_Z 0.3 -76.600 3.91e-25 -17.128
Metro_vs_DEMetro_Z 0.5 -68.487 3.26e-24 -15.314
Metro_vs_DEMetro_Z 0.9 -73.092 9.49e-25 -16.344
Metro_vs_DEMetro_Z 0.99 -40.767 5.81e-20 -9.116
DEMetro_Z_vs_SMC 0.0 47.744 2.97e-21 10.676
DEMetro_Z_vs_SMC 0.3 75.681 4.91e-25 16.923
DEMetro_Z_vs_SMC 0.5 69.462 2.49e-24 15.532
DEMetro_Z_vs_SMC 0.9 79.890 1.76e-25 17.864
DEMetro_Z_vs_SMC 0.99 61.124 2.8e-23 13.668
HMC_vs_DEMetro_Z 0.0 -47.767 2.94e-21 -10.681
HMC_vs_DEMetro_Z 0.3 -75.788 4.78e-25 -16.947
HMC_vs_DEMetro_Z 0.5 -69.673 2.35e-24 -15.579
HMC_vs_DEMetro_Z 0.9 -76.212 4.3e-25 -17.041
HMC_vs_DEMetro_Z 0.99 -62.215 2e-23 -13.912
HMC_vs_Metro 0.0 -16.557 9.57e-13 -3.702
HMC_vs_Metro 0.3 -4.675 0.000165 -1.045
HMC_vs_Metro 0.5 -4.927 9.36e-05 -1.102
HMC_vs_Metro 0.9 -4.869 0.000107 -1.089
HMC_vs_Metro 0.99 -6.160 6.41e-06 -1.377
HMC_vs_SMC 0.0 -1.736 0.0988 -0.388
HMC_vs_SMC 0.3 1.792 0.0892 0.401
HMC_vs_SMC 0.5 3.815 0.00117 0.853
HMC_vs_SMC 0.9 7.412 5.11e-07 1.657
HMC_vs_SMC 0.99 7.223 7.39e-07 1.615
Metro_vs_SMC 0.0 15.020 5.38e-12 3.359
Metro_vs_SMC 0.3 5.029 7.45e-05 1.124
Metro_vs_SMC 0.5 5.622 2.02e-05 1.257
Metro_vs_SMC 0.9 7.218 7.46e-07 1.614
Metro_vs_SMC 0.99 7.098 9.45e-07 1.587
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.029 0.029 0.002 -0.095
HMC 0.3 0.032 0.028 0.002 2.585
HMC 0.5 0.035 0.028 0.005 1.518
HMC 0.9 0.102 0.024 0.006 14.088
HMC 0.99 0.126 0.025 0.011 9.426
SMC 0.0 0.030 0.029 0.002 0.525
SMC 0.3 0.030 0.028 0.002 1.072
SMC 0.5 0.027 0.028 0.005 -0.126
SMC 0.9 0.023 0.024 0.006 -0.194
SMC 0.99 0.024 0.025 0.011 -0.101
Metro 0.0 0.040 0.029 0.002 6.912
Metro 0.3 0.064 0.028 0.002 21.500
Metro 0.5 0.104 0.028 0.005 16.468
Metro 0.9 0.310 0.024 0.006 51.614
Metro 0.99 0.883 0.025 0.011 80.330
DEMetro_Z 0.0 9.865 0.029 0.002 5926.234
DEMetro_Z 0.3 10.790 0.028 0.002 6357.251
DEMetro_Z 0.5 10.797 0.028 0.005 2342.786
DEMetro_Z 0.9 10.273 0.024 0.006 1850.420
DEMetro_Z 0.99 9.530 0.025 0.011 890.174
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.217 0.233 -0.317
HMC 0.3 2.588 0.0167 2.117
HMC 0.5 3.468 0.00177 1.813
HMC 0.9 7.354 5.12e-07 17.398
HMC 0.99 9.186 1.04e-08 10.525
SMC 0.0 1.124 0.27 0.477
SMC 0.3 2.021 0.0526 0.947
SMC 0.5 -0.303 0.763 -0.083
SMC 0.9 0.012 0.991 0.005
SMC 0.99 -0.369 0.714 -0.109
Metro 0.0 15.708 5.36e-17 6.257
Metro 0.3 5.426 3e-05 18.167
Metro 0.5 5.743 1.49e-05 17.632
Metro 0.9 8.135 1.29e-07 61.772
Metro 0.99 10.706 1.69e-09 68.489
DEMetro_Z 0.0 64.681 8.61e-24 403.669
DEMetro_Z 0.3 83.682 5.93e-26 396.127
DEMetro_Z 0.5 68.315 2.15e-24 210.010
DEMetro_Z 0.9 63.459 8.7e-24 192.063
DEMetro_Z 0.99 70.713 1.46e-25 94.880
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 65.737 7.07e-24 14.699
DEMetro_Z_vs_SMC 0.3 82.442 9.71e-26 18.435
DEMetro_Z_vs_SMC 0.5 69.248 2.64e-24 15.484
DEMetro_Z_vs_SMC 0.9 64.299 1.07e-23 14.378
DEMetro_Z_vs_SMC 0.99 69.947 2.18e-24 15.641
HMC_vs_Metro 0.0 -17.508 3.52e-13 -3.915
HMC_vs_Metro 0.3 -4.944 9.01e-05 -1.106
HMC_vs_Metro 0.5 -4.959 8.71e-05 -1.109
HMC_vs_Metro 0.9 -5.662 1.85e-05 -1.266
HMC_vs_Metro 0.99 -8.919 3.22e-08 -1.994
Metro_vs_DEMetro_Z 0.0 -63.564 1.34e-23 -14.213
Metro_vs_DEMetro_Z 0.3 -61.312 2.64e-23 -13.710
Metro_vs_DEMetro_Z 0.5 -51.297 7.67e-22 -11.470
Metro_vs_DEMetro_Z 0.9 -13.805 2.35e-11 -3.087
Metro_vs_DEMetro_Z 0.99 -3.993 0.000779 -0.893
HMC_vs_SMC 0.0 -2.000 0.06 -0.447
HMC_vs_SMC 0.3 1.534 0.142 0.343
HMC_vs_SMC 0.5 3.827 0.00114 0.856
HMC_vs_SMC 0.9 7.865 2.16e-07 1.759
HMC_vs_SMC 0.99 9.052 2.55e-08 2.024
Metro_vs_SMC 0.0 12.585 1.15e-10 2.814
Metro_vs_SMC 0.3 5.208 5.01e-05 1.164
Metro_vs_SMC 0.5 5.711 1.67e-05 1.277
Metro_vs_SMC 0.9 8.080 1.45e-07 1.807
Metro_vs_SMC 0.99 10.772 1.57e-09 2.409
HMC_vs_DEMetro_Z 0.0 -64.318 1.07e-23 -14.382
HMC_vs_DEMetro_Z 0.3 -79.815 1.79e-25 -17.847
HMC_vs_DEMetro_Z 0.5 -66.095 6.38e-24 -14.779
HMC_vs_DEMetro_Z 0.9 -45.039 8.92e-21 -10.071
HMC_vs_DEMetro_Z 0.99 -50.422 1.06e-21 -11.275
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.014 0.014 0.001 -0.317
HMC 0.3 0.017 0.014 0.001 2.117
HMC 0.5 0.020 0.015 0.003 1.813
HMC 0.9 0.065 0.013 0.003 17.398
HMC 0.99 0.076 0.014 0.006 10.525
SMC 0.0 0.015 0.014 0.001 0.477
SMC 0.3 0.015 0.014 0.001 0.947
SMC 0.5 0.014 0.015 0.003 -0.083
SMC 0.9 0.013 0.013 0.003 0.005
SMC 0.99 0.014 0.014 0.006 -0.109
Metro 0.0 0.023 0.014 0.001 6.257
Metro 0.3 0.039 0.014 0.001 18.167
Metro 0.5 0.063 0.015 0.003 17.632
Metro 0.9 0.197 0.013 0.003 61.772
Metro 0.99 0.419 0.014 0.006 68.489
DEMetro_Z 0.0 0.588 0.014 0.001 403.669
DEMetro_Z 0.3 0.561 0.014 0.001 396.127
DEMetro_Z 0.5 0.587 0.015 0.003 210.010
DEMetro_Z 0.9 0.585 0.013 0.003 192.063
DEMetro_Z 0.99 0.575 0.014 0.006 94.880
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -4.549 6.33e-05 -1.256
HMC 0.3 2.361 0.0261 1.351
HMC 0.5 3.019 0.0055 1.593
HMC 0.9 3.422 0.00274 5.599
HMC 0.99 3.606 0.00178 5.525
SMC 0.0 -0.871 0.389 -0.288
SMC 0.3 0.624 0.537 0.274
SMC 0.5 0.008 0.994 0.002
SMC 0.9 -0.961 0.343 -0.317
SMC 0.99 0.627 0.535 0.200
Metro 0.0 12.718 1.41e-14 4.874
Metro 0.3 6.473 2.92e-06 12.415
Metro 0.5 7.179 7.06e-07 15.244
Metro 0.9 5.629 1.98e-05 43.131
Metro 0.99 6.536 2.92e-06 90.252
DEMetro_Z 0.0 24.191 9.77e-16 3800.529
DEMetro_Z 0.3 22.861 2.77e-15 4104.403
DEMetro_Z 0.5 31.626 6.76e-18 1622.585
DEMetro_Z 0.9 30.516 1.31e-17 1137.494
DEMetro_Z 0.99 27.888 6.99e-17 565.433
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -24.197 9.73e-16 -5.411
HMC_vs_DEMetro_Z 0.3 -22.851 2.79e-15 -5.110
HMC_vs_DEMetro_Z 0.5 -31.632 6.74e-18 -7.073
HMC_vs_DEMetro_Z 0.9 -30.393 1.42e-17 -6.796
HMC_vs_DEMetro_Z 0.99 -28.026 6.42e-17 -6.267
Metro_vs_SMC 0.0 16.962 6.22e-13 3.793
Metro_vs_SMC 0.3 6.548 2.86e-06 1.464
Metro_vs_SMC 0.5 6.914 1.36e-06 1.546
Metro_vs_SMC 0.9 5.707 1.68e-05 1.276
Metro_vs_SMC 0.99 6.502 3.14e-06 1.454
Metro_vs_DEMetro_Z 0.0 -24.170 9.93e-16 -5.405
Metro_vs_DEMetro_Z 0.3 -22.775 2.97e-15 -5.093
Metro_vs_DEMetro_Z 0.5 -31.636 6.72e-18 -7.074
Metro_vs_DEMetro_Z 0.9 -28.688 4.16e-17 -6.415
Metro_vs_DEMetro_Z 0.99 -17.663 3.01e-13 -3.950
HMC_vs_Metro 0.0 -19.438 5.34e-14 -4.347
HMC_vs_Metro 0.3 -5.747 1.54e-05 -1.285
HMC_vs_Metro 0.5 -5.912 1.08e-05 -1.322
HMC_vs_Metro 0.9 -5.193 5.18e-05 -1.161
HMC_vs_Metro 0.99 -5.760 1.5e-05 -1.288
HMC_vs_SMC 0.0 -3.962 0.000836 -0.886
HMC_vs_SMC 0.3 1.625 0.121 0.363
HMC_vs_SMC 0.5 3.382 0.00313 0.756
HMC_vs_SMC 0.9 3.836 0.00111 0.858
HMC_vs_SMC 0.99 3.384 0.00311 0.757
DEMetro_Z_vs_SMC 0.0 24.193 9.76e-16 5.410
DEMetro_Z_vs_SMC 0.3 22.864 2.76e-15 5.113
DEMetro_Z_vs_SMC 0.5 31.619 6.79e-18 7.070
DEMetro_Z_vs_SMC 0.9 30.491 1.34e-17 6.818
DEMetro_Z_vs_SMC 0.99 28.004 6.51e-17 6.262
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.019 0.023 0.003 -1.256
HMC 0.3 0.025 0.021 0.003 1.351
HMC 0.5 0.034 0.022 0.008 1.593
HMC 0.9 0.075 0.020 0.010 5.599
HMC 0.99 0.115 0.020 0.017 5.525
SMC 0.0 0.022 0.023 0.003 -0.288
SMC 0.3 0.022 0.021 0.003 0.274
SMC 0.5 0.022 0.022 0.008 0.002
SMC 0.9 0.017 0.020 0.010 -0.317
SMC 0.99 0.024 0.020 0.017 0.200
Metro 0.0 0.037 0.023 0.003 4.874
Metro 0.3 0.058 0.021 0.003 12.415
Metro 0.5 0.138 0.022 0.008 15.244
Metro 0.9 0.447 0.020 0.010 43.131
Metro 0.99 1.574 0.020 0.017 90.252
DEMetro_Z 0.0 10.826 0.023 0.003 3800.529
DEMetro_Z 0.3 12.181 0.021 0.003 4104.403
DEMetro_Z 0.5 12.383 0.022 0.008 1622.585
DEMetro_Z 0.9 11.287 0.020 0.010 1137.494
DEMetro_Z 0.99 9.751 0.020 0.017 565.433
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 7.671 6.23e-09 2.974
HMC 0.3 3.030 0.00479 1.259
HMC 0.5 3.424 0.00192 1.706
HMC 0.9 5.110 5.68e-05 9.223
HMC 0.99 3.113 0.0057 12.524
SMC 0.0 -0.261 0.795 -0.099
SMC 0.3 -0.696 0.491 -0.204
SMC 0.5 -0.108 0.915 -0.030
SMC 0.9 1.950 0.0588 0.679
SMC 0.99 -1.125 0.268 -0.373
Metro 0.0 11.465 1.4e-12 5.113
Metro 0.3 8.797 1.05e-08 6.934
Metro 0.5 6.568 1.97e-06 8.065
Metro 0.9 7.489 4.18e-07 25.742
Metro 0.99 24.574 4.34e-16 53.291
DEMetro_Z 0.0 8.273 1.01e-07 4989.047
DEMetro_Z 0.3 12.419 1.45e-10 5354.728
DEMetro_Z 0.5 8.520 6.5e-08 2386.024
DEMetro_Z 0.9 10.352 3e-09 1829.836
DEMetro_Z 0.99 14.557 9.31e-12 1482.951
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 7.865 2.16e-07 1.759
HMC_vs_SMC 0.3 4.064 0.000662 0.909
HMC_vs_SMC 0.5 3.731 0.00142 0.834
HMC_vs_SMC 0.9 4.861 0.000109 1.087
HMC_vs_SMC 0.99 3.317 0.00363 0.742
Metro_vs_DEMetro_Z 0.0 -8.265 1.03e-07 -1.848
Metro_vs_DEMetro_Z 0.3 -12.408 1.47e-10 -2.774
Metro_vs_DEMetro_Z 0.5 -8.504 6.69e-08 -1.901
Metro_vs_DEMetro_Z 0.9 -10.186 3.91e-09 -2.278
Metro_vs_DEMetro_Z 0.99 -14.001 1.84e-11 -3.131
HMC_vs_Metro 0.0 -5.103 6.32e-05 -1.141
HMC_vs_Metro 0.3 -7.012 1.12e-06 -1.568
HMC_vs_Metro 0.5 -5.093 6.46e-05 -1.139
HMC_vs_Metro 0.9 -3.845 0.00109 -0.860
HMC_vs_Metro 0.99 -7.762 2.61e-07 -1.736
HMC_vs_DEMetro_Z 0.0 -8.267 1.02e-07 -1.849
HMC_vs_DEMetro_Z 0.3 -12.415 1.46e-10 -2.776
HMC_vs_DEMetro_Z 0.5 -8.512 6.59e-08 -1.903
HMC_vs_DEMetro_Z 0.9 -10.298 3.27e-09 -2.303
HMC_vs_DEMetro_Z 0.99 -14.635 8.49e-12 -3.272
Metro_vs_SMC 0.0 14.026 1.78e-11 3.136
Metro_vs_SMC 0.3 9.217 1.93e-08 2.061
Metro_vs_SMC 0.5 6.458 3.44e-06 1.444
Metro_vs_SMC 0.9 7.393 5.3e-07 1.653
Metro_vs_SMC 0.99 24.597 7.19e-16 5.500
DEMetro_Z_vs_SMC 0.0 8.271 1.02e-07 1.850
DEMetro_Z_vs_SMC 0.3 12.420 1.45e-10 2.777
DEMetro_Z_vs_SMC 0.5 8.521 6.49e-08 1.905
DEMetro_Z_vs_SMC 0.9 10.346 3.04e-09 2.313
DEMetro_Z_vs_SMC 0.99 14.577 9.09e-12 3.260
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.044 0.032 0.004 2.974
HMC 0.3 0.038 0.032 0.004 1.259
HMC 0.5 0.045 0.031 0.008 1.706
HMC 0.9 0.139 0.024 0.012 9.223
HMC 0.99 0.209 0.026 0.015 12.524
SMC 0.0 0.031 0.032 0.004 -0.099
SMC 0.3 0.031 0.032 0.004 -0.204
SMC 0.5 0.031 0.031 0.008 -0.030
SMC 0.9 0.033 0.024 0.012 0.679
SMC 0.99 0.020 0.026 0.015 -0.373
Metro 0.0 0.052 0.032 0.004 5.113
Metro 0.3 0.061 0.032 0.004 6.934
Metro 0.5 0.095 0.031 0.008 8.065
Metro 0.9 0.344 0.024 0.012 25.742
Metro 0.99 0.806 0.026 0.015 53.291
DEMetro_Z 0.0 19.971 0.032 0.004 4989.047
DEMetro_Z 0.3 22.248 0.032 0.004 5354.728
DEMetro_Z 0.5 18.801 0.031 0.008 2386.024
DEMetro_Z 0.9 22.732 0.024 0.012 1829.836
DEMetro_Z 0.99 21.752 0.026 0.015 1482.951
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.398 0.693 0.112
HMC 0.3 3.650 0.00116 2.053
HMC 0.5 4.371 0.00016 2.241
HMC 0.9 4.633 0.000172 9.867
HMC 0.99 5.278 3.95e-05 10.408
SMC 0.0 -0.345 0.732 -0.109
SMC 0.3 0.505 0.617 0.222
SMC 0.5 -0.113 0.911 -0.030
SMC 0.9 0.140 0.89 0.046
SMC 0.99 0.310 0.758 0.094
Metro 0.0 15.040 9.45e-16 6.603
Metro 0.3 7.827 2e-07 16.965
Metro 0.5 7.831 2.05e-07 19.262
Metro 0.9 6.073 7.66e-06 64.349
Metro 0.99 7.722 2.82e-07 123.279
DEMetro_Z 0.0 26.890 1.38e-16 5430.913
DEMetro_Z 0.3 25.479 3.75e-16 5841.761
DEMetro_Z 0.5 30.963 1e-17 2227.015
DEMetro_Z 0.9 27.656 8.21e-17 1699.151
DEMetro_Z 0.99 29.131 3.12e-17 767.285
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -26.858 1.41e-16 -6.006
Metro_vs_DEMetro_Z 0.3 -25.373 4.05e-16 -5.674
Metro_vs_DEMetro_Z 0.5 -30.973 9.98e-18 -6.926
Metro_vs_DEMetro_Z 0.9 -26.442 1.89e-16 -5.913
Metro_vs_DEMetro_Z 0.99 -18.991 8.15e-14 -4.246
DEMetro_Z_vs_SMC 0.0 26.891 1.38e-16 6.013
DEMetro_Z_vs_SMC 0.3 25.488 3.73e-16 5.699
DEMetro_Z_vs_SMC 0.5 30.957 1.01e-17 6.922
DEMetro_Z_vs_SMC 0.9 27.636 8.33e-17 6.180
DEMetro_Z_vs_SMC 0.99 29.221 2.95e-17 6.534
HMC_vs_DEMetro_Z 0.0 -26.887 1.39e-16 -6.012
HMC_vs_DEMetro_Z 0.3 -25.468 3.78e-16 -5.695
HMC_vs_DEMetro_Z 0.5 -30.949 1.01e-17 -6.920
HMC_vs_DEMetro_Z 0.9 -27.479 9.25e-17 -6.145
HMC_vs_DEMetro_Z 0.99 -29.297 2.81e-17 -6.551
HMC_vs_Metro 0.0 -16.645 8.71e-13 -3.722
HMC_vs_Metro 0.3 -7.169 8.21e-07 -1.603
HMC_vs_Metro 0.5 -6.537 2.92e-06 -1.462
HMC_vs_Metro 0.9 -5.426 3.1e-05 -1.213
HMC_vs_Metro 0.99 -6.758 1.86e-06 -1.511
HMC_vs_SMC 0.0 0.822 0.421 0.184
HMC_vs_SMC 0.3 2.534 0.0202 0.567
HMC_vs_SMC 0.5 5.001 7.94e-05 1.118
HMC_vs_SMC 0.9 4.803 0.000124 1.074
HMC_vs_SMC 0.99 5.180 5.33e-05 1.158
Metro_vs_SMC 0.0 15.875 2.02e-12 3.550
Metro_vs_SMC 0.3 7.931 1.91e-07 1.773
Metro_vs_SMC 0.5 7.697 2.96e-07 1.721
Metro_vs_SMC 0.9 6.109 7.12e-06 1.366
Metro_vs_SMC 0.99 7.700 2.94e-07 1.722
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.029 0.029 0.002 0.112
HMC 0.3 0.031 0.028 0.002 2.053
HMC 0.5 0.038 0.028 0.005 2.241
HMC 0.9 0.079 0.024 0.006 9.867
HMC 0.99 0.136 0.025 0.011 10.408
SMC 0.0 0.029 0.029 0.002 -0.109
SMC 0.3 0.028 0.028 0.002 0.222
SMC 0.5 0.028 0.028 0.005 -0.030
SMC 0.9 0.025 0.024 0.006 0.046
SMC 0.99 0.026 0.025 0.011 0.094
Metro 0.0 0.040 0.029 0.002 6.603
Metro 0.3 0.057 0.028 0.002 16.965
Metro 0.5 0.116 0.028 0.005 19.262
Metro 0.9 0.381 0.024 0.006 64.349
Metro 0.99 1.341 0.025 0.011 123.279
DEMetro_Z 0.0 9.043 0.029 0.002 5430.913
DEMetro_Z 0.3 9.917 0.028 0.002 5841.761
DEMetro_Z 0.5 10.265 0.028 0.005 2227.015
DEMetro_Z 0.9 9.435 0.024 0.006 1699.151
DEMetro_Z 0.99 8.218 0.025 0.011 767.285
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.574 0.125 -0.413
HMC 0.3 2.768 0.0102 1.497
HMC 0.5 4.453 0.00014 2.444
HMC 0.9 4.871 0.000102 13.055
HMC 0.99 5.254 4.29e-05 12.822
SMC 0.0 -0.593 0.557 -0.202
SMC 0.3 0.600 0.553 0.259
SMC 0.5 -0.271 0.788 -0.073
SMC 0.9 1.273 0.213 0.570
SMC 0.99 -0.030 0.976 -0.010
Metro 0.0 13.359 9.94e-15 5.526
Metro 0.3 7.883 1.67e-07 13.947
Metro 0.5 7.813 2.15e-07 20.551
Metro 0.9 7.550 3.89e-07 77.732
Metro 0.99 12.553 1.19e-10 125.394
DEMetro_Z 0.0 62.903 1.56e-23 650.738
DEMetro_Z 0.3 50.983 8.43e-22 668.194
DEMetro_Z 0.5 48.038 2.46e-21 345.227
DEMetro_Z 0.9 84.149 4.77e-26 322.554
DEMetro_Z 0.99 85.166 1.17e-26 152.700
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 62.843 1.66e-23 14.052
DEMetro_Z_vs_SMC 0.3 51.013 8.52e-22 11.407
DEMetro_Z_vs_SMC 0.5 47.741 2.97e-21 10.675
DEMetro_Z_vs_SMC 0.9 83.491 7.64e-26 18.669
DEMetro_Z_vs_SMC 0.99 85.895 4.46e-26 19.207
HMC_vs_Metro 0.0 -15.612 2.72e-12 -3.491
HMC_vs_Metro 0.3 -7.290 6.48e-07 -1.630
HMC_vs_Metro 0.5 -6.699 2.1e-06 -1.498
HMC_vs_Metro 0.9 -6.672 2.22e-06 -1.492
HMC_vs_Metro 0.99 -9.928 5.91e-09 -2.220
Metro_vs_DEMetro_Z 0.0 -63.007 1.58e-23 -14.089
Metro_vs_DEMetro_Z 0.3 -52.827 4.41e-22 -11.812
Metro_vs_DEMetro_Z 0.5 -44.285 1.23e-20 -9.902
Metro_vs_DEMetro_Z 0.9 -21.873 6.22e-15 -4.891
Metro_vs_DEMetro_Z 0.99 -2.644 0.016 -0.591
HMC_vs_SMC 0.0 -0.767 0.453 -0.171
HMC_vs_SMC 0.3 1.867 0.0775 0.417
HMC_vs_SMC 0.5 5.222 4.86e-05 1.168
HMC_vs_SMC 0.9 4.830 0.000116 1.080
HMC_vs_SMC 0.99 5.219 4.88e-05 1.167
Metro_vs_SMC 0.0 15.814 2.17e-12 3.536
Metro_vs_SMC 0.3 7.965 1.79e-07 1.781
Metro_vs_SMC 0.5 7.693 2.98e-07 1.720
Metro_vs_SMC 0.9 7.587 3.65e-07 1.696
Metro_vs_SMC 0.99 12.501 1.29e-10 2.795
HMC_vs_DEMetro_Z 0.0 -62.887 1.64e-23 -14.062
HMC_vs_DEMetro_Z 0.3 -51.666 6.7e-22 -11.553
HMC_vs_DEMetro_Z 0.5 -47.112 3.82e-21 -10.535
HMC_vs_DEMetro_Z 0.9 -61.016 2.89e-23 -13.644
HMC_vs_DEMetro_Z 0.99 -48.190 2.49e-21 -10.776
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.014 0.014 0.001 -0.413
HMC 0.3 0.016 0.014 0.001 1.497
HMC 0.5 0.021 0.015 0.003 2.444
HMC 0.9 0.052 0.013 0.003 13.055
HMC 0.99 0.090 0.014 0.006 12.822
SMC 0.0 0.014 0.014 0.001 -0.202
SMC 0.3 0.014 0.014 0.001 0.259
SMC 0.5 0.015 0.015 0.003 -0.073
SMC 0.9 0.015 0.013 0.003 0.570
SMC 0.99 0.014 0.014 0.006 -0.010
Metro 0.0 0.022 0.014 0.001 5.526
Metro 0.3 0.033 0.014 0.001 13.947
Metro 0.5 0.071 0.015 0.003 20.551
Metro 0.9 0.244 0.013 0.003 77.732
Metro 0.99 0.755 0.014 0.006 125.394
DEMetro_Z 0.0 0.939 0.014 0.001 650.738
DEMetro_Z 0.3 0.936 0.014 0.001 668.194
DEMetro_Z 0.5 0.956 0.015 0.003 345.227
DEMetro_Z 0.9 0.973 0.013 0.003 322.554
DEMetro_Z 0.99 0.916 0.014 0.006 152.700
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_heavy_Tails (MvStudentT, correlation, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.086 0.932 0.025
HMC 0.3 1.609 0.117 0.628
HMC 0.5 1.053 0.3 0.406
HMC 0.9 2.511 0.0174 1.089
HMC 0.99 1.568 0.126 0.612
SMC 0.0 3.996 0.000352 1.666
SMC 0.3 1.935 0.0621 0.844
SMC 0.5 6.218 1.02e-06 3.104
SMC 0.9 3.371 0.00194 1.387
SMC 0.99 2.629 0.0133 1.173
Metro 0.0 1.573 0.132 2.512
Metro 0.3 1.600 0.126 3.763
Metro 0.5 3.295 0.00284 1.829
Metro 0.9 3.124 0.00525 3.663
Metro 0.99 4.815 0.000118 20.176
DEMetro_Z 0.0 3.563 0.00147 2.032
DEMetro_Z 0.3 4.652 0.000115 3.511
DEMetro_Z 0.5 2.717 0.0133 3.751
DEMetro_Z 0.9 4.279 0.000297 3.357
DEMetro_Z 0.99 2.746 0.0118 2.227
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -3.555 0.00211 -0.795
HMC_vs_DEMetro_Z 0.3 -3.280 0.00394 -0.733
HMC_vs_DEMetro_Z 0.5 -2.326 0.0313 -0.520
HMC_vs_DEMetro_Z 0.9 -3.001 0.00735 -0.671
HMC_vs_DEMetro_Z 0.99 -2.085 0.0508 -0.466
Metro_vs_SMC 0.0 0.521 0.608 0.116
Metro_vs_SMC 0.3 1.250 0.226 0.280
Metro_vs_SMC 0.5 -1.570 0.133 -0.351
Metro_vs_SMC 0.9 1.841 0.0813 0.412
Metro_vs_SMC 0.99 4.533 0.000228 1.013
Metro_vs_DEMetro_Z 0.0 0.284 0.779 0.064
Metro_vs_DEMetro_Z 0.3 0.099 0.922 0.022
Metro_vs_DEMetro_Z 0.5 -1.740 0.098 -0.389
Metro_vs_DEMetro_Z 0.9 0.210 0.836 0.047
Metro_vs_DEMetro_Z 0.99 4.372 0.000328 0.978
HMC_vs_Metro 0.0 -1.602 0.126 -0.358
HMC_vs_Metro 0.3 -1.334 0.198 -0.298
HMC_vs_Metro 0.5 -2.280 0.0343 -0.510
HMC_vs_Metro 0.9 -2.163 0.0435 -0.484
HMC_vs_Metro 0.99 -4.647 0.000176 -1.039
HMC_vs_SMC 0.0 -5.107 6.26e-05 -1.142
HMC_vs_SMC 0.3 -0.363 0.721 -0.081
HMC_vs_SMC 0.5 -4.675 0.000165 -1.045
HMC_vs_SMC 0.9 -0.657 0.519 -0.147
HMC_vs_SMC 0.99 -1.107 0.282 -0.247
DEMetro_Z_vs_SMC 0.0 0.559 0.583 0.125
DEMetro_Z_vs_SMC 0.3 3.461 0.00262 0.774
DEMetro_Z_vs_SMC 0.5 0.445 0.661 0.100
DEMetro_Z_vs_SMC 0.9 2.381 0.0279 0.532
DEMetro_Z_vs_SMC 0.99 1.168 0.257 0.261
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.067 0.066 0.039 0.025
HMC 0.3 0.059 0.045 0.023 0.628
HMC 0.5 0.080 0.062 0.045 0.406
HMC 0.9 0.103 0.055 0.044 1.089
HMC 0.99 0.092 0.060 0.052 0.612
SMC 0.0 0.132 0.066 0.039 1.666
SMC 0.3 0.064 0.045 0.023 0.844
SMC 0.5 0.201 0.062 0.045 3.104
SMC 0.9 0.117 0.055 0.044 1.387
SMC 0.99 0.121 0.060 0.052 1.173
Metro 0.0 0.165 0.066 0.039 2.512
Metro 0.3 0.131 0.045 0.023 3.763
Metro 0.5 0.144 0.062 0.045 1.829
Metro 0.9 0.217 0.055 0.044 3.663
Metro 0.99 1.105 0.060 0.052 20.176
DEMetro_Z 0.0 0.146 0.066 0.039 2.032
DEMetro_Z 0.3 0.125 0.045 0.023 3.511
DEMetro_Z 0.5 0.230 0.062 0.045 3.751
DEMetro_Z 0.9 0.203 0.055 0.044 3.357
DEMetro_Z 0.99 0.176 0.060 0.052 2.227
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.780 0.441 -0.201
HMC 0.3 -0.699 0.491 -0.169
HMC 0.5 0.359 0.723 0.196
HMC 0.9 1.429 0.169 11.089
HMC 0.99 -0.061 0.952 -0.018
SMC 0.0 1.411 0.169 0.356
SMC 0.3 0.768 0.449 0.189
SMC 0.5 8.666 4.4e-09 4.980
SMC 0.9 2.461 0.0236 16.080
SMC 0.99 3.873 0.000423 1.135
Metro 0.0 0.514 0.611 0.205
Metro 0.3 0.433 0.667 0.135
Metro 0.5 0.021 0.984 0.011
Metro 0.9 1.240 0.23 9.471
Metro 0.99 1.949 0.0609 0.909
DEMetro_Z 0.0 -0.509 0.614 -0.136
DEMetro_Z 0.3 -0.098 0.923 -0.024
DEMetro_Z 0.5 1.054 0.305 2.507
DEMetro_Z 0.9 1.323 0.202 10.220
DEMetro_Z 0.99 -0.709 0.486 -0.163
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -4.234 0.000449 -0.947
HMC_vs_SMC 0.3 -2.313 0.0321 -0.517
HMC_vs_SMC 0.5 -6.627 2.43e-06 -1.482
HMC_vs_SMC 0.9 -1.973 0.0632 -0.441
HMC_vs_SMC 0.99 -4.750 0.000139 -1.062
Metro_vs_DEMetro_Z 0.0 1.099 0.286 0.246
Metro_vs_DEMetro_Z 0.3 0.778 0.446 0.174
Metro_vs_DEMetro_Z 0.5 -1.061 0.302 -0.237
Metro_vs_DEMetro_Z 0.9 -0.433 0.67 -0.097
Metro_vs_DEMetro_Z 0.99 2.595 0.0178 0.580
HMC_vs_Metro 0.0 -1.273 0.218 -0.285
HMC_vs_Metro 0.3 -1.487 0.153 -0.333
HMC_vs_Metro 0.5 1.405 0.176 0.314
HMC_vs_Metro 0.9 0.738 0.47 0.165
HMC_vs_Metro 0.99 -1.881 0.0754 -0.421
HMC_vs_DEMetro_Z 0.0 -1.012 0.324 -0.226
HMC_vs_DEMetro_Z 0.3 -5.112 6.19e-05 -1.143
HMC_vs_DEMetro_Z 0.5 -0.984 0.337 -0.220
HMC_vs_DEMetro_Z 0.9 0.868 0.396 0.194
HMC_vs_DEMetro_Z 0.99 0.766 0.453 0.171
Metro_vs_SMC 0.0 -0.415 0.683 -0.093
Metro_vs_SMC 0.3 -0.210 0.836 -0.047
Metro_vs_SMC 0.5 -7.072 9.94e-07 -1.581
Metro_vs_SMC 0.9 -3.634 0.00177 -0.813
Metro_vs_SMC 0.99 -0.505 0.619 -0.113
DEMetro_Z_vs_SMC 0.0 -2.918 0.00881 -0.653
DEMetro_Z_vs_SMC 0.3 -1.329 0.199 -0.297
DEMetro_Z_vs_SMC 0.5 -1.050 0.307 -0.235
DEMetro_Z_vs_SMC 0.9 -2.856 0.0101 -0.639
DEMetro_Z_vs_SMC 0.99 -6.207 5.8e-06 -1.388
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 6.243 9.309 15.244 -0.201
HMC 0.3 4.677 6.558 11.160 -0.169
HMC 0.5 9.380 7.776 8.203 0.196
HMC 0.9 21.206 2.247 1.710 11.089
HMC 0.99 7.300 7.581 15.891 -0.018
SMC 0.0 14.740 9.309 15.244 0.356
SMC 0.3 8.667 6.558 11.160 0.189
SMC 0.5 48.624 7.776 8.203 4.980
SMC 0.9 29.738 2.247 1.710 16.080
SMC 0.99 25.613 7.581 15.891 1.135
Metro 0.0 12.441 9.309 15.244 0.205
Metro 0.3 8.060 6.558 11.160 0.135
Metro 0.5 7.870 7.776 8.203 0.011
Metro 0.9 18.440 2.247 1.710 9.471
Metro 0.99 22.019 7.581 15.891 0.909
DEMetro_Z 0.0 7.237 9.309 15.244 -0.136
DEMetro_Z 0.3 6.295 6.558 11.160 -0.024
DEMetro_Z 0.5 28.338 7.776 8.203 2.507
DEMetro_Z 0.9 19.720 2.247 1.710 10.220
DEMetro_Z 0.99 4.997 7.581 15.891 -0.163
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.935 0.0606 0.633
HMC 0.3 2.819 0.00857 1.332
HMC 0.5 2.582 0.0148 1.136
HMC 0.9 3.431 0.00253 3.529
HMC 0.99 3.512 0.00156 1.804
SMC 0.0 9.996 4.1e-09 19.627
SMC 0.3 9.422 1.14e-08 21.260
SMC 0.5 13.994 1.69e-11 56.364
SMC 0.9 11.097 8.56e-10 35.040
SMC 0.99 10.770 1.38e-09 31.461
Metro 0.0 3.554 0.00198 4.804
Metro 0.3 2.929 0.00844 5.620
Metro 0.5 7.101 1.42e-07 3.880
Metro 0.9 5.703 1.43e-05 8.413
Metro 0.99 5.851 1.22e-05 35.993
DEMetro_Z 0.0 8.441 2.09e-09 3.857
DEMetro_Z 0.3 11.037 3.32e-11 6.375
DEMetro_Z 0.5 2.230 0.0379 11.429
DEMetro_Z 0.9 5.092 5.64e-05 7.433
DEMetro_Z 0.99 6.765 6.88e-07 4.940
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 0.689 0.499 0.154
Metro_vs_DEMetro_Z 0.3 -0.375 0.712 -0.084
Metro_vs_DEMetro_Z 0.5 -1.532 0.142 -0.343
Metro_vs_DEMetro_Z 0.9 0.447 0.66 0.100
Metro_vs_DEMetro_Z 0.99 5.276 4.31e-05 1.180
DEMetro_Z_vs_SMC 0.0 -7.447 4.78e-07 -1.665
DEMetro_Z_vs_SMC 0.3 -5.896 1.12e-05 -1.318
DEMetro_Z_vs_SMC 0.5 -7.673 3.1e-07 -1.716
DEMetro_Z_vs_SMC 0.9 -8.643 5.22e-08 -1.933
DEMetro_Z_vs_SMC 0.99 -8.376 8.42e-08 -1.873
HMC_vs_DEMetro_Z 0.0 -7.962 1.8e-07 -1.780
HMC_vs_DEMetro_Z 0.3 -6.908 1.38e-06 -1.545
HMC_vs_DEMetro_Z 0.5 -2.010 0.0588 -0.450
HMC_vs_DEMetro_Z 0.9 -3.593 0.00194 -0.803
HMC_vs_DEMetro_Z 0.99 -3.454 0.00266 -0.772
HMC_vs_Metro 0.0 -3.170 0.00504 -0.709
HMC_vs_Metro 0.3 -2.254 0.0362 -0.504
HMC_vs_Metro 0.5 -6.387 3.98e-06 -1.428
HMC_vs_Metro 0.9 -2.753 0.0127 -0.615
HMC_vs_Metro 0.99 -5.422 3.13e-05 -1.212
HMC_vs_SMC 0.0 -10.070 4.7e-09 -2.252
HMC_vs_SMC 0.3 -8.479 6.99e-08 -1.896
HMC_vs_SMC 0.5 -13.349 4.2e-11 -2.985
HMC_vs_SMC 0.9 -9.359 1.51e-08 -2.093
HMC_vs_SMC 0.99 -10.574 2.12e-09 -2.364
Metro_vs_SMC 0.0 -5.423 3.12e-05 -1.213
Metro_vs_SMC 0.3 -5.129 5.97e-05 -1.147
Metro_vs_SMC 0.5 -12.958 7.01e-11 -2.897
Metro_vs_SMC 0.9 -7.676 3.08e-07 -1.717
Metro_vs_SMC 0.99 0.641 0.529 0.143
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.148 0.124 0.038 0.633
HMC 0.3 0.146 0.115 0.024 1.332
HMC 0.5 0.162 0.123 0.034 1.136
HMC 0.9 0.210 0.106 0.029 3.529
HMC 0.99 0.195 0.119 0.042 1.804
SMC 0.0 0.863 0.124 0.038 19.627
SMC 0.3 0.615 0.115 0.024 21.260
SMC 0.5 2.057 0.123 0.034 56.364
SMC 0.9 1.131 0.106 0.029 35.040
SMC 0.99 1.436 0.119 0.042 31.461
Metro 0.0 0.305 0.124 0.038 4.804
Metro 0.3 0.247 0.115 0.024 5.620
Metro 0.5 0.256 0.123 0.034 3.880
Metro 0.9 0.352 0.106 0.029 8.413
Metro 0.99 1.626 0.119 0.042 35.993
DEMetro_Z 0.0 0.269 0.124 0.038 3.857
DEMetro_Z 0.3 0.265 0.115 0.024 6.375
DEMetro_Z 0.5 0.515 0.123 0.034 11.429
DEMetro_Z 0.9 0.324 0.106 0.029 7.433
DEMetro_Z 0.99 0.326 0.119 0.042 4.940
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.691 0.0118 1.327
HMC 0.3 2.393 0.024 1.284
HMC 0.5 2.876 0.00667 1.004
HMC 0.9 4.124 0.000353 2.411
HMC 0.99 4.770 4.7e-05 2.236
SMC 0.0 12.676 8.09e-11 30.347
SMC 0.3 11.681 3.3e-10 28.025
SMC 0.5 20.633 1.48e-14 68.089
SMC 0.9 14.484 8.82e-12 47.536
SMC 0.99 14.681 6.57e-12 40.991
Metro 0.0 9.504 6.22e-10 5.334
Metro 0.3 5.615 9.89e-06 3.936
Metro 0.5 7.603 1.85e-07 7.602
Metro 0.9 8.601 3.58e-08 11.413
Metro 0.99 8.717 4.46e-08 47.588
DEMetro_Z 0.0 9.169 2.25e-09 5.768
DEMetro_Z 0.3 7.495 2.09e-07 6.978
DEMetro_Z 0.5 5.186 4.9e-05 10.819
DEMetro_Z 0.9 9.618 2.48e-09 7.975
DEMetro_Z 0.99 7.346 2.49e-07 6.246
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 -9.351 1.53e-08 -2.091
DEMetro_Z_vs_SMC 0.3 -7.067 1e-06 -1.580
DEMetro_Z_vs_SMC 0.5 -18.216 1.73e-13 -4.073
DEMetro_Z_vs_SMC 0.9 -12.763 9.08e-11 -2.854
DEMetro_Z_vs_SMC 0.99 -11.152 8.84e-10 -2.494
HMC_vs_Metro 0.0 -5.703 1.69e-05 -1.275
HMC_vs_Metro 0.3 -3.385 0.00311 -0.757
HMC_vs_Metro 0.5 -6.399 3.89e-06 -1.431
HMC_vs_Metro 0.9 -6.457 3.45e-06 -1.444
HMC_vs_Metro 0.99 -8.404 8e-08 -1.879
Metro_vs_DEMetro_Z 0.0 -0.703 0.49 -0.157
Metro_vs_DEMetro_Z 0.3 -2.495 0.022 -0.558
Metro_vs_DEMetro_Z 0.5 -1.264 0.222 -0.283
Metro_vs_DEMetro_Z 0.9 1.957 0.0652 0.438
Metro_vs_DEMetro_Z 0.99 7.749 2.68e-07 1.733
HMC_vs_SMC 0.0 -12.080 2.31e-10 -2.701
HMC_vs_SMC 0.3 -10.833 1.43e-09 -2.422
HMC_vs_SMC 0.5 -20.461 2.1e-14 -4.575
HMC_vs_SMC 0.9 -13.460 3.64e-11 -3.010
HMC_vs_SMC 0.99 -13.994 1.86e-11 -3.129
Metro_vs_SMC 0.0 -9.719 8.31e-09 -2.173
Metro_vs_SMC 0.3 -10.093 4.53e-09 -2.257
Metro_vs_SMC 0.5 -17.540 3.41e-13 -3.922
Metro_vs_SMC 0.9 -11.236 7.8e-10 -2.513
Metro_vs_SMC 0.99 0.993 0.333 0.222
HMC_vs_DEMetro_Z 0.0 -7.206 7.64e-07 -1.611
HMC_vs_DEMetro_Z 0.3 -5.031 7.41e-05 -1.125
HMC_vs_DEMetro_Z 0.5 -4.560 0.000214 -1.020
HMC_vs_DEMetro_Z 0.9 -5.424 3.11e-05 -1.213
HMC_vs_DEMetro_Z 0.99 -5.300 4.09e-05 -1.185
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.021 0.014 0.005 1.327
HMC 0.3 0.020 0.015 0.004 1.284
HMC 0.5 0.019 0.015 0.004 1.004
HMC 0.9 0.023 0.013 0.004 2.411
HMC 0.99 0.028 0.015 0.006 2.236
SMC 0.0 0.156 0.014 0.005 30.347
SMC 0.3 0.121 0.015 0.004 28.025
SMC 0.5 0.282 0.015 0.004 68.089
SMC 0.9 0.194 0.013 0.004 47.536
SMC 0.99 0.246 0.015 0.006 40.991
Metro 0.0 0.039 0.014 0.005 5.334
Metro 0.3 0.030 0.015 0.004 3.936
Metro 0.5 0.045 0.015 0.004 7.602
Metro 0.9 0.057 0.013 0.004 11.413
Metro 0.99 0.283 0.015 0.006 47.588
DEMetro_Z 0.0 0.041 0.014 0.005 5.768
DEMetro_Z 0.3 0.041 0.015 0.004 6.978
DEMetro_Z 0.5 0.057 0.015 0.004 10.819
DEMetro_Z 0.9 0.044 0.013 0.004 7.975
DEMetro_Z 0.99 0.050 0.015 0.006 6.246
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.237 0.814 0.075
HMC 0.3 2.391 0.0264 2.592
HMC 0.5 -0.122 0.904 -0.038
HMC 0.9 2.081 0.0465 1.003
HMC 0.99 1.520 0.139 0.712
SMC 0.0 1.835 0.0765 0.838
SMC 0.3 3.022 0.00559 1.694
SMC 0.5 4.351 0.000266 3.846
SMC 0.9 2.276 0.0295 0.927
SMC 0.99 2.619 0.0143 1.381
Metro 0.0 2.963 0.00536 1.064
Metro 0.3 3.038 0.00626 3.067
Metro 0.5 3.827 0.000657 1.878
Metro 0.9 3.713 0.00129 3.718
Metro 0.99 1.792 0.089 74.629
DEMetro_Z 0.0 3.120 0.00473 2.117
DEMetro_Z 0.3 3.154 0.00501 4.603
DEMetro_Z 0.5 2.826 0.00988 2.406
DEMetro_Z 0.9 3.014 0.00622 2.220
DEMetro_Z 0.99 2.553 0.0173 1.566
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -3.200 0.00471 -0.716
HMC_vs_DEMetro_Z 0.3 -1.872 0.0767 -0.418
HMC_vs_DEMetro_Z 0.5 -3.119 0.00565 -0.697
HMC_vs_DEMetro_Z 0.9 -1.369 0.187 -0.306
HMC_vs_DEMetro_Z 0.99 -1.134 0.271 -0.254
Metro_vs_SMC 0.0 0.565 0.579 0.126
Metro_vs_SMC 0.3 1.129 0.273 0.253
Metro_vs_SMC 0.5 -2.177 0.0423 -0.487
Metro_vs_SMC 0.9 2.986 0.0076 0.668
Metro_vs_SMC 0.99 1.761 0.0944 0.394
Metro_vs_DEMetro_Z 0.0 -1.439 0.167 -0.322
Metro_vs_DEMetro_Z 0.3 -0.900 0.379 -0.201
Metro_vs_DEMetro_Z 0.5 -0.568 0.577 -0.127
Metro_vs_DEMetro_Z 0.9 1.156 0.262 0.259
Metro_vs_DEMetro_Z 0.99 1.757 0.0951 0.393
HMC_vs_Metro 0.0 -2.521 0.0208 -0.564
HMC_vs_Metro 0.3 -0.377 0.71 -0.084
HMC_vs_Metro 0.5 -3.857 0.00106 -0.862
HMC_vs_Metro 0.9 -2.506 0.0215 -0.560
HMC_vs_Metro 0.99 -1.782 0.0908 -0.398
HMC_vs_SMC 0.0 -1.528 0.143 -0.342
HMC_vs_SMC 0.3 0.651 0.523 0.145
HMC_vs_SMC 0.5 -4.300 0.000386 -0.962
HMC_vs_SMC 0.9 0.144 0.887 0.032
HMC_vs_SMC 0.99 -1.146 0.266 -0.256
DEMetro_Z_vs_SMC 0.0 1.634 0.119 0.365
DEMetro_Z_vs_SMC 0.3 1.661 0.113 0.371
DEMetro_Z_vs_SMC 0.5 -1.105 0.283 -0.247
DEMetro_Z_vs_SMC 0.9 1.806 0.0868 0.404
DEMetro_Z_vs_SMC 0.99 0.219 0.829 0.049
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.069 0.066 0.039 0.075
HMC 0.3 0.104 0.045 0.023 2.592
HMC 0.5 0.060 0.062 0.045 -0.038
HMC 0.9 0.100 0.055 0.044 1.003
HMC 0.99 0.097 0.060 0.052 0.712
SMC 0.0 0.099 0.066 0.039 0.838
SMC 0.3 0.084 0.045 0.023 1.694
SMC 0.5 0.234 0.062 0.045 3.846
SMC 0.9 0.096 0.055 0.044 0.927
SMC 0.99 0.132 0.060 0.052 1.381
Metro 0.0 0.108 0.066 0.039 1.064
Metro 0.3 0.115 0.045 0.023 3.067
Metro 0.5 0.146 0.062 0.045 1.878
Metro 0.9 0.219 0.055 0.044 3.718
Metro 0.99 3.926 0.060 0.052 74.629
DEMetro_Z 0.0 0.149 0.066 0.039 2.117
DEMetro_Z 0.3 0.150 0.045 0.023 4.603
DEMetro_Z 0.5 0.170 0.062 0.045 2.406
DEMetro_Z 0.9 0.153 0.055 0.044 2.220
DEMetro_Z 0.99 0.141 0.060 0.052 1.566
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.519 0.607 -0.142
HMC 0.3 -0.686 0.499 -0.163
HMC 0.5 -0.039 0.969 -0.022
HMC 0.9 1.344 0.195 10.580
HMC 0.99 -1.091 0.287 -0.252
SMC 0.0 -0.862 0.396 -0.213
SMC 0.3 -0.577 0.57 -0.136
SMC 0.5 2.625 0.0143 1.478
SMC 0.9 1.550 0.138 11.162
SMC 0.99 0.992 0.329 0.252
Metro 0.0 -0.769 0.447 -0.204
Metro 0.3 -0.401 0.692 -0.096
Metro 0.5 0.260 0.797 0.141
Metro 0.9 1.204 0.243 9.110
Metro 0.99 1.420 0.172 14.987
DEMetro_Z 0.0 -0.314 0.755 -0.084
DEMetro_Z 0.3 -0.101 0.921 -0.024
DEMetro_Z 0.5 0.153 0.879 0.083
DEMetro_Z 0.9 1.232 0.233 9.415
DEMetro_Z 0.99 -0.980 0.338 -0.227
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 0.895 0.382 0.200
HMC_vs_SMC 0.3 -0.558 0.583 -0.125
HMC_vs_SMC 0.5 -3.566 0.00206 -0.797
HMC_vs_SMC 0.9 -0.267 0.793 -0.060
HMC_vs_SMC 0.99 -3.854 0.00107 -0.862
Metro_vs_DEMetro_Z 0.0 -3.025 0.00696 -0.677
Metro_vs_DEMetro_Z 0.3 -1.243 0.229 -0.278
Metro_vs_DEMetro_Z 0.5 0.640 0.53 0.143
Metro_vs_DEMetro_Z 0.9 -0.523 0.607 -0.117
Metro_vs_DEMetro_Z 0.99 1.440 0.166 0.322
HMC_vs_Metro 0.0 0.793 0.438 0.177
HMC_vs_Metro 0.3 -1.729 0.1 -0.387
HMC_vs_Metro 0.5 -2.801 0.0114 -0.626
HMC_vs_Metro 0.9 0.763 0.455 0.171
HMC_vs_Metro 0.99 -1.442 0.165 -0.323
HMC_vs_DEMetro_Z 0.0 -0.651 0.523 -0.146
HMC_vs_DEMetro_Z 0.3 -2.597 0.0177 -0.581
HMC_vs_DEMetro_Z 0.5 -1.433 0.168 -0.320
HMC_vs_DEMetro_Z 0.9 0.580 0.568 0.130
HMC_vs_DEMetro_Z 0.99 -0.763 0.455 -0.171
Metro_vs_SMC 0.0 0.132 0.896 0.030
Metro_vs_SMC 0.3 0.858 0.402 0.192
Metro_vs_SMC 0.5 -3.354 0.00334 -0.750
Metro_vs_SMC 0.9 -2.480 0.0227 -0.554
Metro_vs_SMC 0.99 1.394 0.18 0.312
DEMetro_Z_vs_SMC 0.0 1.616 0.123 0.361
DEMetro_Z_vs_SMC 0.3 1.392 0.18 0.311
DEMetro_Z_vs_SMC 0.5 -3.351 0.00336 -0.749
DEMetro_Z_vs_SMC 0.9 -1.585 0.129 -0.354
DEMetro_Z_vs_SMC 0.99 -3.439 0.00275 -0.769
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 7.150 9.309 15.244 -0.142
HMC 0.3 4.738 6.558 11.160 -0.163
HMC 0.5 7.599 7.776 8.203 -0.022
HMC 0.9 20.335 2.247 1.710 10.580
HMC 0.99 3.575 7.581 15.891 -0.252
SMC 0.0 6.060 9.309 15.244 -0.213
SMC 0.3 5.042 6.558 11.160 -0.136
SMC 0.5 19.897 7.776 8.203 1.478
SMC 0.9 21.330 2.247 1.710 11.162
SMC 0.99 11.591 7.581 15.891 0.252
Metro 0.0 6.194 9.309 15.244 -0.204
Metro 0.3 5.488 6.558 11.160 -0.096
Metro 0.5 8.933 7.776 8.203 0.141
Metro 0.9 17.822 2.247 1.710 9.110
Metro 0.99 245.732 7.581 15.891 14.987
DEMetro_Z 0.0 8.031 9.309 15.244 -0.084
DEMetro_Z 0.3 6.286 6.558 11.160 -0.024
DEMetro_Z 0.5 8.456 7.776 8.203 0.083
DEMetro_Z 0.9 18.344 2.247 1.710 9.415
DEMetro_Z 0.99 3.979 7.581 15.891 -0.227
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.246 0.0306 0.740
HMC 0.3 2.646 0.0153 3.125
HMC 0.5 2.478 0.018 0.881
HMC 0.9 4.300 0.000285 3.438
HMC 0.99 3.530 0.00136 1.607
SMC 0.0 5.450 2.52e-05 8.123
SMC 0.3 5.039 6.77e-05 10.027
SMC 0.5 7.171 7.89e-07 28.875
SMC 0.9 7.409 4.56e-07 16.842
SMC 0.99 6.864 1.37e-06 16.573
Metro 0.0 6.589 9.16e-08 2.003
Metro 0.3 4.309 0.000325 4.946
Metro 0.5 6.591 6.76e-07 3.978
Metro 0.9 9.789 2.48e-09 9.216
Metro 0.99 1.912 0.071 100.681
DEMetro_Z 0.0 7.979 1.99e-08 4.531
DEMetro_Z 0.3 4.381 0.000297 7.175
DEMetro_Z 0.5 6.138 3.67e-06 5.219
DEMetro_Z 0.9 7.310 2.78e-07 6.337
DEMetro_Z 0.99 5.045 3.63e-05 3.223
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -4.612 0.00019 -1.031
Metro_vs_DEMetro_Z 0.3 -1.078 0.295 -0.241
Metro_vs_DEMetro_Z 0.5 -1.058 0.303 -0.237
Metro_vs_DEMetro_Z 0.9 1.986 0.0617 0.444
Metro_vs_DEMetro_Z 0.99 1.848 0.0803 0.413
DEMetro_Z_vs_SMC 0.0 -2.266 0.0353 -0.507
DEMetro_Z_vs_SMC 0.3 -0.987 0.336 -0.221
DEMetro_Z_vs_SMC 0.5 -5.526 2.49e-05 -1.236
DEMetro_Z_vs_SMC 0.9 -4.342 0.000351 -0.971
DEMetro_Z_vs_SMC 0.99 -5.355 3.62e-05 -1.197
HMC_vs_DEMetro_Z 0.0 -7.155 8.44e-07 -1.600
HMC_vs_DEMetro_Z 0.3 -2.755 0.0126 -0.616
HMC_vs_DEMetro_Z 0.5 -5.749 1.54e-05 -1.286
HMC_vs_DEMetro_Z 0.9 -2.409 0.0263 -0.539
HMC_vs_DEMetro_Z 0.99 -2.041 0.0554 -0.456
HMC_vs_Metro 0.0 -3.839 0.00111 -0.858
HMC_vs_Metro 0.3 -1.127 0.274 -0.252
HMC_vs_Metro 0.5 -4.669 0.000167 -1.044
HMC_vs_Metro 0.9 -4.936 9.18e-05 -1.104
HMC_vs_Metro 0.99 -1.884 0.075 -0.421
HMC_vs_SMC 0.0 -5.258 4.48e-05 -1.176
HMC_vs_SMC 0.3 -2.756 0.0126 -0.616
HMC_vs_SMC 0.5 -7.025 1.09e-06 -1.571
HMC_vs_SMC 0.9 -5.543 2.4e-05 -1.239
HMC_vs_SMC 0.99 -6.401 3.87e-06 -1.431
Metro_vs_SMC 0.0 -4.279 0.000405 -0.957
Metro_vs_SMC 0.3 -2.161 0.0437 -0.483
Metro_vs_SMC 0.5 -6.515 3.06e-06 -1.457
Metro_vs_SMC 0.9 -3.746 0.00137 -0.838
Metro_vs_SMC 0.99 1.570 0.133 0.351
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.152 0.124 0.038 0.740
HMC 0.3 0.189 0.115 0.024 3.125
HMC 0.5 0.153 0.123 0.034 0.881
HMC 0.9 0.207 0.106 0.029 3.438
HMC 0.99 0.186 0.119 0.042 1.607
SMC 0.0 0.430 0.124 0.038 8.123
SMC 0.3 0.351 0.115 0.024 10.027
SMC 0.5 1.114 0.123 0.034 28.875
SMC 0.9 0.599 0.106 0.029 16.842
SMC 0.99 0.813 0.119 0.042 16.573
Metro 0.0 0.200 0.124 0.038 2.003
Metro 0.3 0.231 0.115 0.024 4.946
Metro 0.5 0.260 0.123 0.034 3.978
Metro 0.9 0.376 0.106 0.029 9.216
Metro 0.99 4.333 0.119 0.042 100.681
DEMetro_Z 0.0 0.295 0.124 0.038 4.531
DEMetro_Z 0.3 0.284 0.115 0.024 7.175
DEMetro_Z 0.5 0.302 0.123 0.034 5.219
DEMetro_Z 0.9 0.292 0.106 0.029 6.337
DEMetro_Z 0.99 0.254 0.119 0.042 3.223
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.653 0.0118 0.965
HMC 0.3 1.531 0.142 4.499
HMC 0.5 3.007 0.00526 1.349
HMC 0.9 6.941 1.96e-07 3.707
HMC 0.99 3.491 0.00203 2.708
SMC 0.0 7.246 6.38e-07 17.533
SMC 0.3 5.435 2.93e-05 16.812
SMC 0.5 10.831 1.36e-09 49.433
SMC 0.9 8.058 1.43e-07 29.870
SMC 0.99 9.313 1.5e-08 30.465
Metro 0.0 7.866 1.51e-08 3.957
Metro 0.3 8.030 1.23e-08 4.207
Metro 0.5 6.952 8.18e-07 7.858
Metro 0.9 6.790 1.57e-06 15.068
Metro 0.99 5.864 1.2e-05 55.497
DEMetro_Z 0.0 9.310 1.92e-09 6.038
DEMetro_Z 0.3 6.934 4.96e-07 5.219
DEMetro_Z 0.5 6.357 2.7e-06 6.478
DEMetro_Z 0.9 8.347 3.27e-08 7.278
DEMetro_Z 0.99 6.269 2.46e-06 4.937
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 -4.728 0.000146 -1.057
DEMetro_Z_vs_SMC 0.3 -3.425 0.00284 -0.766
DEMetro_Z_vs_SMC 0.5 -9.246 1.83e-08 -2.067
DEMetro_Z_vs_SMC 0.9 -5.986 9.25e-06 -1.339
DEMetro_Z_vs_SMC 0.99 -7.722 2.82e-07 -1.727
HMC_vs_Metro 0.0 -5.090 6.51e-05 -1.138
HMC_vs_Metro 0.3 0.098 0.923 0.022
HMC_vs_Metro 0.5 -5.776 1.45e-05 -1.292
HMC_vs_Metro 0.9 -4.853 0.00011 -1.085
HMC_vs_Metro 0.99 -5.440 3e-05 -1.217
Metro_vs_DEMetro_Z 0.0 -2.614 0.0171 -0.585
Metro_vs_DEMetro_Z 0.3 -1.065 0.3 -0.238
Metro_vs_DEMetro_Z 0.5 0.972 0.343 0.217
Metro_vs_DEMetro_Z 0.9 3.223 0.00448 0.721
Metro_vs_DEMetro_Z 0.99 5.152 5.67e-05 1.152
HMC_vs_SMC 0.0 -6.785 1.76e-06 -1.517
HMC_vs_SMC 0.3 -2.622 0.0168 -0.586
HMC_vs_SMC 0.5 -10.552 2.2e-09 -2.360
HMC_vs_SMC 0.9 -6.713 2.04e-06 -1.501
HMC_vs_SMC 0.99 -9.259 1.79e-08 -2.070
Metro_vs_SMC 0.0 -5.424 3.11e-05 -1.213
Metro_vs_SMC 0.3 -4.254 0.000429 -0.951
Metro_vs_SMC 0.5 -10.012 5.16e-09 -2.239
Metro_vs_SMC 0.9 -4.110 0.000596 -0.919
Metro_vs_SMC 0.99 2.123 0.0471 0.475
HMC_vs_DEMetro_Z 0.0 -8.958 3e-08 -2.003
HMC_vs_DEMetro_Z 0.3 -0.252 0.803 -0.056
HMC_vs_DEMetro_Z 0.5 -5.972 9.54e-06 -1.335
HMC_vs_DEMetro_Z 0.9 -4.066 0.000659 -0.909
HMC_vs_DEMetro_Z 0.99 -2.066 0.0527 -0.462
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.019 0.014 0.005 0.965
HMC 0.3 0.032 0.015 0.004 4.499
HMC 0.5 0.020 0.015 0.004 1.349
HMC 0.9 0.028 0.013 0.004 3.707
HMC 0.99 0.030 0.015 0.006 2.708
SMC 0.0 0.096 0.014 0.005 17.533
SMC 0.3 0.079 0.015 0.004 16.812
SMC 0.5 0.209 0.015 0.004 49.433
SMC 0.9 0.127 0.013 0.004 29.870
SMC 0.99 0.187 0.015 0.006 30.465
Metro 0.0 0.033 0.014 0.005 3.957
Metro 0.3 0.031 0.015 0.004 4.207
Metro 0.5 0.046 0.015 0.004 7.858
Metro 0.9 0.071 0.013 0.004 15.068
Metro 0.99 0.327 0.015 0.006 55.497
DEMetro_Z 0.0 0.043 0.014 0.005 6.038
DEMetro_Z 0.3 0.035 0.015 0.004 5.219
DEMetro_Z 0.5 0.040 0.015 0.004 6.478
DEMetro_Z 0.9 0.041 0.013 0.004 7.278
DEMetro_Z 0.99 0.043 0.015 0.006 4.937
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_high_Multimodality (Mixture, correlation, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.646 0.000174 19.987
HMC 0.3 4.217 0.000466 33.526
HMC 0.5 5.419 3.1e-05 24.886
HMC 0.9 4.491 0.000248 22.867
HMC 0.99 5.252 4.52e-05 42.278
SMC 0.0 0.346 0.732 0.134
SMC 0.3 0.993 0.328 0.380
SMC 0.5 1.316 0.196 0.403
SMC 0.9 -0.409 0.685 -0.114
SMC 0.99 1.583 0.126 0.948
Metro 0.0 3.596 0.00191 14.990
Metro 0.3 4.145 0.000548 30.857
Metro 0.5 5.351 3.58e-05 21.743
Metro 0.9 4.738 0.000141 21.303
Metro 0.99 5.589 2.16e-05 42.859
DEMetro_Z 0.0 6.973 1.13e-06 19.654
DEMetro_Z 0.3 4.964 8.55e-05 27.936
DEMetro_Z 0.5 5.785 1.4e-05 31.600
DEMetro_Z 0.9 4.960 8.56e-05 22.093
DEMetro_Z 0.99 6.161 6.35e-06 51.519
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 0.081 0.936 0.018
HMC_vs_DEMetro_Z 0.3 0.516 0.612 0.115
HMC_vs_DEMetro_Z 0.5 -0.837 0.413 -0.187
HMC_vs_DEMetro_Z 0.9 0.123 0.904 0.027
HMC_vs_DEMetro_Z 0.99 -0.832 0.416 -0.186
Metro_vs_SMC 0.0 3.585 0.00197 0.802
Metro_vs_SMC 0.3 4.079 0.00064 0.912
Metro_vs_SMC 0.5 5.286 4.21e-05 1.182
Metro_vs_SMC 0.9 4.783 0.000129 1.070
Metro_vs_SMC 0.99 5.452 2.93e-05 1.219
Metro_vs_DEMetro_Z 0.0 -1.136 0.27 -0.254
Metro_vs_DEMetro_Z 0.3 0.295 0.771 0.066
Metro_vs_DEMetro_Z 0.5 -1.279 0.216 -0.286
Metro_vs_DEMetro_Z 0.9 -0.136 0.893 -0.030
Metro_vs_DEMetro_Z 0.99 -0.932 0.363 -0.208
HMC_vs_Metro 0.0 1.787 0.0899 0.400
HMC_vs_Metro 0.3 0.382 0.706 0.085
HMC_vs_Metro 0.5 0.620 0.543 0.139
HMC_vs_Metro 0.9 0.330 0.745 0.074
HMC_vs_Metro 0.99 -0.053 0.958 -0.012
HMC_vs_SMC 0.0 4.637 0.00018 1.037
HMC_vs_SMC 0.3 4.125 0.000576 0.922
HMC_vs_SMC 0.5 5.383 3.41e-05 1.204
HMC_vs_SMC 0.9 4.574 0.000207 1.023
HMC_vs_SMC 0.99 5.221 4.86e-05 1.168
DEMetro_Z_vs_SMC 0.0 6.848 1.55e-06 1.531
DEMetro_Z_vs_SMC 0.3 4.842 0.000113 1.083
DEMetro_Z_vs_SMC 0.5 5.747 1.54e-05 1.285
DEMetro_Z_vs_SMC 0.9 4.985 8.22e-05 1.115
DEMetro_Z_vs_SMC 0.99 6.271 5.07e-06 1.402
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.308 0.089 0.061 19.987
HMC 0.3 1.750 0.074 0.050 33.526
HMC 0.5 1.621 0.061 0.063 24.886
HMC 0.9 1.759 0.094 0.073 22.867
HMC 0.99 1.731 0.063 0.039 42.278
SMC 0.0 0.097 0.089 0.061 0.134
SMC 0.3 0.093 0.074 0.050 0.380
SMC 0.5 0.087 0.061 0.063 0.403
SMC 0.9 0.086 0.094 0.073 -0.114
SMC 0.99 0.100 0.063 0.039 0.948
Metro 0.0 1.003 0.089 0.061 14.990
Metro 0.3 1.616 0.074 0.050 30.857
Metro 0.5 1.424 0.061 0.063 21.743
Metro 0.9 1.645 0.094 0.073 21.303
Metro 0.99 1.754 0.063 0.039 42.859
DEMetro_Z 0.0 1.288 0.089 0.061 19.654
DEMetro_Z 0.3 1.470 0.074 0.050 27.936
DEMetro_Z 0.5 2.041 0.061 0.063 31.600
DEMetro_Z 0.9 1.702 0.094 0.073 22.093
DEMetro_Z 0.99 2.096 0.063 0.039 51.519
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.759 0.000135 29.361
HMC 0.3 3.319 0.0036 62.876
HMC 0.5 3.960 0.000839 61.399
HMC 0.9 3.459 0.00263 76.998
HMC 0.99 3.645 0.00172 57.387
SMC 0.0 -0.916 0.366 -0.257
SMC 0.3 -0.246 0.807 -0.079
SMC 0.5 0.424 0.674 0.168
SMC 0.9 1.810 0.0801 0.805
SMC 0.99 0.559 0.58 0.202
Metro 0.0 3.741 0.00138 22.257
Metro 0.3 3.202 0.00469 54.169
Metro 0.5 5.637 1.94e-05 47.506
Metro 0.9 3.700 0.00152 70.026
Metro 0.99 4.160 0.000531 64.135
DEMetro_Z 0.0 4.409 0.000299 22.883
DEMetro_Z 0.3 2.949 0.00824 36.970
DEMetro_Z 0.5 4.167 0.000523 94.488
DEMetro_Z 0.9 3.501 0.00239 66.823
DEMetro_Z 0.99 4.212 0.000471 74.390
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 4.854 0.00011 1.085
HMC_vs_SMC 0.3 3.322 0.00358 0.743
HMC_vs_SMC 0.5 3.928 0.000903 0.878
HMC_vs_SMC 0.9 3.415 0.0029 0.764
HMC_vs_SMC 0.99 3.639 0.00174 0.814
Metro_vs_DEMetro_Z 0.0 -0.093 0.927 -0.021
Metro_vs_DEMetro_Z 0.3 0.728 0.476 0.163
Metro_vs_DEMetro_Z 0.5 -1.758 0.0948 -0.393
Metro_vs_DEMetro_Z 0.9 0.116 0.909 0.026
Metro_vs_DEMetro_Z 0.99 -0.812 0.427 -0.182
HMC_vs_Metro 0.0 1.649 0.116 0.369
HMC_vs_Metro 0.3 0.422 0.678 0.094
HMC_vs_Metro 0.5 0.884 0.388 0.198
HMC_vs_Metro 0.9 0.461 0.65 0.103
HMC_vs_Metro 0.99 -0.304 0.764 -0.068
HMC_vs_DEMetro_Z 0.0 0.958 0.35 0.214
HMC_vs_DEMetro_Z 0.3 1.026 0.318 0.229
HMC_vs_DEMetro_Z 0.5 -1.074 0.296 -0.240
HMC_vs_DEMetro_Z 0.9 0.340 0.737 0.076
HMC_vs_DEMetro_Z 0.99 -0.709 0.487 -0.159
Metro_vs_SMC 0.0 3.839 0.00111 0.858
Metro_vs_SMC 0.3 3.211 0.0046 0.718
Metro_vs_SMC 0.5 5.615 2.05e-05 1.256
Metro_vs_SMC 0.9 3.643 0.00173 0.815
Metro_vs_SMC 0.99 4.165 0.000526 0.931
DEMetro_Z_vs_SMC 0.0 4.538 0.000225 1.015
DEMetro_Z_vs_SMC 0.3 2.973 0.00782 0.665
DEMetro_Z_vs_SMC 0.5 4.142 0.000554 0.926
DEMetro_Z_vs_SMC 0.9 3.458 0.00264 0.773
DEMetro_Z_vs_SMC 0.99 4.222 0.000462 0.944
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.142 0.191 0.135 29.361
HMC 0.3 8.653 0.190 0.135 62.876
HMC 0.5 6.014 0.153 0.095 61.399
HMC 0.9 7.900 0.150 0.101 76.998
HMC 0.99 7.049 0.170 0.120 57.387
SMC 0.0 0.156 0.191 0.135 -0.257
SMC 0.3 0.180 0.190 0.135 -0.079
SMC 0.5 0.169 0.153 0.095 0.168
SMC 0.9 0.231 0.150 0.101 0.805
SMC 0.99 0.194 0.170 0.120 0.202
Metro 0.0 3.186 0.191 0.135 22.257
Metro 0.3 7.481 0.190 0.135 54.169
Metro 0.5 4.688 0.153 0.095 47.506
Metro 0.9 7.198 0.150 0.101 70.026
Metro 0.99 7.858 0.170 0.120 64.135
DEMetro_Z 0.0 3.270 0.191 0.135 22.883
DEMetro_Z 0.3 5.166 0.190 0.135 36.970
DEMetro_Z 0.5 9.173 0.153 0.095 94.488
DEMetro_Z 0.9 6.876 0.150 0.101 66.823
DEMetro_Z 0.99 9.088 0.170 0.120 74.390
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.663 0.000168 22.529
HMC 0.3 4.083 0.000632 35.588
HMC 0.5 5.425 3.06e-05 26.491
HMC 0.9 4.457 0.000268 25.976
HMC 0.99 5.332 3.79e-05 46.194
SMC 0.0 0.509 0.614 0.202
SMC 0.3 0.857 0.397 0.311
SMC 0.5 1.105 0.276 0.333
SMC 0.9 -0.362 0.719 -0.106
SMC 0.99 1.519 0.142 0.940
Metro 0.0 3.644 0.00172 15.995
Metro 0.3 4.175 0.000512 33.030
Metro 0.5 5.408 3.17e-05 24.409
Metro 0.9 4.863 0.000107 23.833
Metro 0.99 5.795 1.38e-05 48.433
DEMetro_Z 0.0 6.867 1.42e-06 21.553
DEMetro_Z 0.3 4.843 0.000112 29.654
DEMetro_Z 0.5 5.898 1.1e-05 34.601
DEMetro_Z 0.9 4.970 8.41e-05 24.282
DEMetro_Z 0.99 6.047 8.09e-06 54.708
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -1.273 0.218 -0.285
Metro_vs_DEMetro_Z 0.3 0.316 0.756 0.071
Metro_vs_DEMetro_Z 0.5 -1.201 0.244 -0.269
Metro_vs_DEMetro_Z 0.9 -0.069 0.945 -0.015
Metro_vs_DEMetro_Z 0.99 -0.665 0.514 -0.149
DEMetro_Z_vs_SMC 0.0 6.749 1.9e-06 1.509
DEMetro_Z_vs_SMC 0.3 4.759 0.000137 1.064
DEMetro_Z_vs_SMC 0.5 5.862 1.2e-05 1.311
DEMetro_Z_vs_SMC 0.9 4.989 8.15e-05 1.116
DEMetro_Z_vs_SMC 0.99 6.176 6.2e-06 1.381
HMC_vs_DEMetro_Z 0.0 0.211 0.835 0.047
HMC_vs_DEMetro_Z 0.3 0.497 0.625 0.111
HMC_vs_DEMetro_Z 0.5 -0.935 0.361 -0.209
HMC_vs_DEMetro_Z 0.9 0.242 0.812 0.054
HMC_vs_DEMetro_Z 0.99 -0.729 0.475 -0.163
HMC_vs_Metro 0.0 1.947 0.0664 0.435
HMC_vs_Metro 0.3 0.323 0.75 0.072
HMC_vs_Metro 0.5 0.371 0.715 0.083
HMC_vs_Metro 0.9 0.396 0.696 0.089
HMC_vs_Metro 0.99 -0.184 0.856 -0.041
HMC_vs_SMC 0.0 4.653 0.000173 1.040
HMC_vs_SMC 0.3 4.011 0.000747 0.897
HMC_vs_SMC 0.5 5.405 3.24e-05 1.209
HMC_vs_SMC 0.9 4.512 0.000238 1.009
HMC_vs_SMC 0.99 5.330 3.82e-05 1.192
Metro_vs_SMC 0.0 3.635 0.00176 0.813
Metro_vs_SMC 0.3 4.124 0.000577 0.922
Metro_vs_SMC 0.5 5.373 3.48e-05 1.201
Metro_vs_SMC 0.9 4.874 0.000105 1.090
Metro_vs_SMC 0.99 5.690 1.74e-05 1.272
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.196 0.096 0.049 22.529
HMC 0.3 1.585 0.087 0.042 35.588
HMC 0.5 1.421 0.078 0.051 26.491
HMC 0.9 1.600 0.103 0.058 25.976
HMC 0.99 1.590 0.077 0.033 46.194
SMC 0.0 0.106 0.096 0.049 0.202
SMC 0.3 0.100 0.087 0.042 0.311
SMC 0.5 0.095 0.078 0.051 0.333
SMC 0.9 0.096 0.103 0.058 -0.106
SMC 0.99 0.107 0.077 0.033 0.940
Metro 0.0 0.877 0.096 0.049 15.995
Metro 0.3 1.477 0.087 0.042 33.030
Metro 0.5 1.316 0.078 0.051 24.409
Metro 0.9 1.476 0.103 0.058 23.833
Metro 0.99 1.664 0.077 0.033 48.433
DEMetro_Z 0.0 1.148 0.096 0.049 21.553
DEMetro_Z 0.3 1.335 0.087 0.042 29.654
DEMetro_Z 0.5 1.833 0.078 0.051 34.601
DEMetro_Z 0.9 1.502 0.103 0.058 24.282
DEMetro_Z 0.99 1.869 0.077 0.033 54.708
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.672 0.000164 24.183
HMC 0.3 4.302 0.000384 37.951
HMC 0.5 5.487 2.68e-05 29.001
HMC 0.9 4.677 0.000163 24.294
HMC 0.99 5.412 3.18e-05 45.826
SMC 0.0 0.305 0.762 0.121
SMC 0.3 0.953 0.347 0.364
SMC 0.5 1.265 0.214 0.412
SMC 0.9 -0.345 0.732 -0.096
SMC 0.99 1.491 0.149 0.925
Metro 0.0 3.651 0.00169 18.145
Metro 0.3 4.229 0.000453 36.256
Metro 0.5 5.371 3.44e-05 25.596
Metro 0.9 4.825 0.000116 22.965
Metro 0.99 5.783 1.42e-05 48.534
DEMetro_Z 0.0 7.120 8.58e-07 23.781
DEMetro_Z 0.3 5.181 5.27e-05 32.525
DEMetro_Z 0.5 5.905 1.09e-05 36.366
DEMetro_Z 0.9 5.064 6.8e-05 23.395
DEMetro_Z 0.99 6.348 4.3e-06 54.939
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 7.047 1.05e-06 1.576
DEMetro_Z_vs_SMC 0.3 5.091 6.49e-05 1.138
DEMetro_Z_vs_SMC 0.5 5.854 1.23e-05 1.309
DEMetro_Z_vs_SMC 0.9 5.103 6.32e-05 1.141
DEMetro_Z_vs_SMC 0.99 6.466 3.39e-06 1.446
HMC_vs_Metro 0.0 1.826 0.0836 0.408
HMC_vs_Metro 0.3 0.222 0.827 0.050
HMC_vs_Metro 0.5 0.575 0.572 0.129
HMC_vs_Metro 0.9 0.262 0.796 0.059
HMC_vs_Metro 0.99 -0.225 0.824 -0.050
Metro_vs_DEMetro_Z 0.0 -1.164 0.259 -0.260
Metro_vs_DEMetro_Z 0.3 0.334 0.742 0.075
Metro_vs_DEMetro_Z 0.5 -1.224 0.236 -0.274
Metro_vs_DEMetro_Z 0.9 -0.071 0.944 -0.016
Metro_vs_DEMetro_Z 0.99 -0.668 0.512 -0.149
HMC_vs_SMC 0.0 4.679 0.000163 1.046
HMC_vs_SMC 0.3 4.228 0.000456 0.945
HMC_vs_SMC 0.5 5.460 2.87e-05 1.221
HMC_vs_SMC 0.9 4.751 0.000139 1.062
HMC_vs_SMC 0.99 5.421 3.13e-05 1.212
Metro_vs_SMC 0.0 3.655 0.00169 0.817
Metro_vs_SMC 0.3 4.189 0.000498 0.937
Metro_vs_SMC 0.5 5.305 4.04e-05 1.186
Metro_vs_SMC 0.9 4.840 0.000114 1.082
Metro_vs_SMC 0.99 5.666 1.84e-05 1.267
HMC_vs_DEMetro_Z 0.0 0.083 0.935 0.019
HMC_vs_DEMetro_Z 0.3 0.452 0.656 0.101
HMC_vs_DEMetro_Z 0.5 -0.809 0.428 -0.181
HMC_vs_DEMetro_Z 0.9 0.141 0.889 0.032
HMC_vs_DEMetro_Z 0.99 -0.797 0.436 -0.178
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.187 0.012 0.007 24.183
HMC 0.3 0.239 0.011 0.006 37.951
HMC 0.5 0.227 0.009 0.008 29.001
HMC 0.9 0.250 0.013 0.010 24.294
HMC 0.99 0.247 0.009 0.005 45.826
SMC 0.0 0.013 0.012 0.007 0.121
SMC 0.3 0.013 0.011 0.006 0.364
SMC 0.5 0.012 0.009 0.008 0.412
SMC 0.9 0.012 0.013 0.010 -0.096
SMC 0.99 0.013 0.009 0.005 0.925
Metro 0.0 0.144 0.012 0.007 18.145
Metro 0.3 0.229 0.011 0.006 36.256
Metro 0.5 0.202 0.009 0.008 25.596
Metro 0.9 0.237 0.013 0.010 22.965
Metro 0.99 0.261 0.009 0.005 48.534
DEMetro_Z 0.0 0.184 0.012 0.007 23.781
DEMetro_Z 0.3 0.207 0.011 0.006 32.525
DEMetro_Z 0.5 0.283 0.009 0.008 36.366
DEMetro_Z 0.9 0.241 0.013 0.010 23.395
DEMetro_Z 0.99 0.295 0.009 0.005 54.939
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 220.345 6.06e-60 74.195
HMC 0.3 203.371 2.67e-49 90.695
HMC 0.5 235.973 1.29e-61 72.628
HMC 0.9 195.028 1.24e-58 61.681
HMC 0.99 214.236 8.12e-45 114.222
SMC 0.0 -0.031 0.976 -0.010
SMC 0.3 1.597 0.119 0.562
SMC 0.5 0.793 0.433 0.247
SMC 0.9 -0.078 0.939 -0.027
SMC 0.99 2.219 0.0341 0.995
Metro 0.0 45.607 1.68e-21 72.561
Metro 0.3 191.990 8.41e-47 90.527
Metro 0.5 229.596 2.58e-61 73.101
Metro 0.9 155.196 2.33e-49 61.829
Metro 0.99 59.923 1.37e-23 116.636
DEMetro_Z 0.0 11.179 8.2e-10 63.677
DEMetro_Z 0.3 9.459 1.26e-08 73.661
DEMetro_Z 0.5 9.500 1.17e-08 59.057
DEMetro_Z 0.9 178.034 1.04e-55 61.993
DEMetro_Z 0.99 224.143 4.06e-46 115.899
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 1.855 0.0792 0.415
HMC_vs_DEMetro_Z 0.3 2.160 0.0438 0.483
HMC_vs_DEMetro_Z 0.5 2.187 0.0414 0.489
HMC_vs_DEMetro_Z 0.9 -1.315 0.204 -0.294
HMC_vs_DEMetro_Z 0.99 -2.155 0.0442 -0.482
Metro_vs_SMC 0.0 46.692 4.52e-21 10.441
Metro_vs_SMC 0.3 208.613 2.17e-33 46.647
Metro_vs_SMC 0.5 281.458 7.33e-36 62.936
Metro_vs_SMC 0.9 130.986 1.49e-29 29.289
Metro_vs_SMC 0.99 61.530 2.47e-23 13.758
Metro_vs_DEMetro_Z 0.0 1.474 0.157 0.329
Metro_vs_DEMetro_Z 0.3 2.141 0.0455 0.479
Metro_vs_DEMetro_Z 0.5 2.265 0.0354 0.506
Metro_vs_DEMetro_Z 0.9 -0.459 0.651 -0.103
Metro_vs_DEMetro_Z 0.99 0.396 0.697 0.089
HMC_vs_Metro 0.0 1.032 0.315 0.231
HMC_vs_Metro 0.3 0.552 0.587 0.124
HMC_vs_Metro 0.5 -1.770 0.0928 -0.396
HMC_vs_Metro 0.9 -0.443 0.663 -0.099
HMC_vs_Metro 0.99 -1.078 0.294 -0.241
HMC_vs_SMC 0.0 235.552 2.16e-34 52.671
HMC_vs_SMC 0.3 218.223 9.21e-34 48.796
HMC_vs_SMC 0.5 214.995 1.22e-33 48.074
HMC_vs_SMC 0.9 150.083 1.13e-30 33.560
HMC_vs_SMC 0.99 145.562 2.01e-30 32.549
DEMetro_Z_vs_SMC 0.0 10.961 1.18e-09 2.451
DEMetro_Z_vs_SMC 0.3 9.364 1.5e-08 2.094
DEMetro_Z_vs_SMC 0.5 9.477 1.24e-08 2.119
DEMetro_Z_vs_SMC 0.9 130.787 1.53e-29 29.245
DEMetro_Z_vs_SMC 0.99 316.126 8.07e-37 70.688
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.616 0.089 0.061 74.195
HMC 0.3 4.606 0.074 0.050 90.695
HMC 0.5 4.612 0.061 0.063 72.628
HMC 0.9 4.584 0.094 0.073 61.681
HMC 0.99 4.571 0.063 0.039 114.222
SMC 0.0 0.088 0.089 0.061 -0.010
SMC 0.3 0.102 0.074 0.050 0.562
SMC 0.5 0.077 0.061 0.063 0.247
SMC 0.9 0.092 0.094 0.073 -0.027
SMC 0.99 0.102 0.063 0.039 0.995
Metro 0.0 4.516 0.089 0.061 72.561
Metro 0.3 4.598 0.074 0.050 90.527
Metro 0.5 4.642 0.061 0.063 73.101
Metro 0.9 4.595 0.094 0.073 61.829
Metro 0.99 4.666 0.063 0.039 116.636
DEMetro_Z 0.0 3.974 0.089 0.061 63.677
DEMetro_Z 0.3 3.755 0.074 0.050 73.661
DEMetro_Z 0.5 3.762 0.061 0.063 59.057
DEMetro_Z 0.9 4.607 0.094 0.073 61.993
DEMetro_Z 0.99 4.637 0.063 0.039 115.899
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 757.030 8.28e-79 220.550
HMC 0.3 539.147 3.52e-66 220.442
HMC 0.5 710.928 1.08e-66 311.457
HMC 0.9 667.013 2.18e-65 295.034
HMC 0.99 608.754 4.09e-68 247.849
SMC 0.0 -1.771 0.0855 -0.486
SMC 0.3 0.098 0.922 0.032
SMC 0.5 1.884 0.0686 0.788
SMC 0.9 0.513 0.611 0.159
SMC 0.99 0.738 0.465 0.260
Metro 0.0 28.731 3.85e-17 213.058
Metro 0.3 552.862 9.51e-68 220.456
Metro 0.5 719.475 1.98e-67 311.443
Metro 0.9 662.763 5.93e-65 295.400
Metro 0.99 348.360 1.61e-44 247.662
DEMetro_Z 0.0 10.487 2.42e-09 187.919
DEMetro_Z 0.3 8.776 4.12e-08 176.381
DEMetro_Z 0.5 8.769 4.17e-08 249.598
DEMetro_Z 0.9 651.591 5.71e-64 295.361
DEMetro_Z 0.99 590.385 3.22e-66 247.712
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 793.745 2.05e-44 177.487
HMC_vs_SMC 0.3 537.846 3.33e-41 120.266
HMC_vs_SMC 0.5 574.521 9.51e-42 128.467
HMC_vs_SMC 0.9 717.529 1.39e-43 160.444
HMC_vs_SMC 0.99 451.921 9.09e-40 101.053
Metro_vs_DEMetro_Z 0.0 1.254 0.225 0.280
Metro_vs_DEMetro_Z 0.3 2.179 0.0421 0.487
Metro_vs_DEMetro_Z 0.5 2.175 0.0425 0.486
Metro_vs_DEMetro_Z 0.9 0.277 0.785 0.062
Metro_vs_DEMetro_Z 0.99 -0.084 0.934 -0.019
HMC_vs_Metro 0.0 1.003 0.328 0.224
HMC_vs_Metro 0.3 -0.198 0.845 -0.044
HMC_vs_Metro 0.5 0.116 0.909 0.026
HMC_vs_Metro 0.9 -2.618 0.0169 -0.585
HMC_vs_Metro 0.99 0.325 0.749 0.073
HMC_vs_DEMetro_Z 0.0 1.823 0.0841 0.408
HMC_vs_DEMetro_Z 0.3 2.176 0.0424 0.486
HMC_vs_DEMetro_Z 0.5 2.178 0.0422 0.487
HMC_vs_DEMetro_Z 0.9 -3.950 0.00086 -0.883
HMC_vs_DEMetro_Z 0.99 1.299 0.209 0.291
Metro_vs_SMC 0.0 28.703 4.12e-17 6.418
Metro_vs_SMC 0.3 565.285 1.29e-41 126.402
Metro_vs_SMC 0.5 581.126 7.65e-42 129.944
Metro_vs_SMC 0.9 708.188 1.79e-43 158.356
Metro_vs_SMC 0.99 300.632 2.1e-36 67.223
DEMetro_Z_vs_SMC 0.0 10.526 2.29e-09 2.354
DEMetro_Z_vs_SMC 0.3 8.755 4.28e-08 1.958
DEMetro_Z_vs_SMC 0.5 8.732 4.46e-08 1.953
DEMetro_Z_vs_SMC 0.9 683.875 3.47e-43 152.919
DEMetro_Z_vs_SMC 0.99 444.638 1.24e-39 99.424
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 29.872 0.191 0.135 220.550
HMC 0.3 29.862 0.190 0.135 220.442
HMC 0.5 29.886 0.153 0.095 311.457
HMC 0.9 29.845 0.150 0.101 295.034
HMC 0.99 29.883 0.170 0.120 247.849
SMC 0.0 0.125 0.191 0.135 -0.486
SMC 0.3 0.195 0.190 0.135 0.032
SMC 0.5 0.228 0.153 0.095 0.788
SMC 0.9 0.166 0.150 0.101 0.159
SMC 0.99 0.201 0.170 0.120 0.260
Metro 0.0 28.864 0.191 0.135 213.058
Metro 0.3 29.864 0.190 0.135 220.456
Metro 0.5 29.884 0.153 0.095 311.443
Metro 0.9 29.882 0.150 0.101 295.400
Metro 0.99 29.861 0.170 0.120 247.662
DEMetro_Z 0.0 25.480 0.191 0.135 187.919
DEMetro_Z 0.3 23.932 0.190 0.135 176.381
DEMetro_Z 0.5 23.980 0.153 0.095 249.598
DEMetro_Z 0.9 29.878 0.150 0.101 295.361
DEMetro_Z 0.99 29.867 0.170 0.120 247.712
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 59.935 5.15e-24 85.146
HMC 0.3 48.313 9.23e-22 95.823
HMC 0.5 73.028 1.99e-26 79.556
HMC 0.9 74.672 2.44e-27 68.688
HMC 0.99 83.269 8.31e-27 121.065
SMC 0.0 0.178 0.86 0.063
SMC 0.3 1.142 0.261 0.381
SMC 0.5 0.734 0.467 0.239
SMC 0.9 -0.089 0.93 -0.034
SMC 0.99 2.011 0.0534 0.915
Metro 0.0 34.403 7.98e-19 80.247
Metro 0.3 78.112 1.22e-26 96.305
Metro 0.5 56.757 1.41e-23 79.191
Metro 0.9 56.063 1.22e-23 71.856
Metro 0.99 36.740 3.15e-19 128.084
DEMetro_Z 0.0 10.970 1.13e-09 72.489
DEMetro_Z 0.3 9.459 1.26e-08 78.539
DEMetro_Z 0.5 9.419 1.34e-08 67.401
DEMetro_Z 0.9 53.599 3.27e-23 69.923
DEMetro_Z 0.99 62.861 5.35e-24 121.756
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 1.066 0.3 0.238
Metro_vs_DEMetro_Z 0.3 2.162 0.0436 0.483
Metro_vs_DEMetro_Z 0.5 1.642 0.117 0.367
Metro_vs_DEMetro_Z 0.9 1.110 0.281 0.248
Metro_vs_DEMetro_Z 0.99 1.700 0.106 0.380
DEMetro_Z_vs_SMC 0.0 10.756 1.61e-09 2.405
DEMetro_Z_vs_SMC 0.3 9.379 1.46e-08 2.097
DEMetro_Z_vs_SMC 0.5 9.415 1.38e-08 2.105
DEMetro_Z_vs_SMC 0.9 54.579 2.38e-22 12.204
DEMetro_Z_vs_SMC 0.99 64.759 9.39e-24 14.480
HMC_vs_DEMetro_Z 0.0 1.900 0.0727 0.425
HMC_vs_DEMetro_Z 0.3 1.785 0.0902 0.399
HMC_vs_DEMetro_Z 0.5 1.649 0.115 0.369
HMC_vs_DEMetro_Z 0.9 -0.702 0.491 -0.157
HMC_vs_DEMetro_Z 0.99 -0.319 0.753 -0.071
HMC_vs_Metro 0.0 1.537 0.141 0.344
HMC_vs_Metro 0.3 -0.191 0.85 -0.043
HMC_vs_Metro 0.5 0.202 0.842 0.045
HMC_vs_Metro 0.9 -2.175 0.0424 -0.486
HMC_vs_Metro 0.99 -1.956 0.0654 -0.437
HMC_vs_SMC 0.0 53.907 3.01e-22 12.054
HMC_vs_SMC 0.3 49.565 1.47e-21 11.083
HMC_vs_SMC 0.5 69.538 2.44e-24 15.549
HMC_vs_SMC 0.9 69.193 2.68e-24 15.472
HMC_vs_SMC 0.99 76.022 4.51e-25 16.999
Metro_vs_SMC 0.0 34.407 1.4e-18 7.694
Metro_vs_SMC 0.3 71.041 1.63e-24 15.885
Metro_vs_SMC 0.5 54.649 2.32e-22 12.220
Metro_vs_SMC 0.9 53.717 3.21e-22 12.012
Metro_vs_SMC 0.99 38.778 1.49e-19 8.671
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.254 0.096 0.049 85.146
HMC 0.3 4.119 0.087 0.042 95.823
HMC 0.5 4.113 0.078 0.051 79.556
HMC 0.9 4.061 0.103 0.058 68.688
HMC 0.99 4.044 0.077 0.033 121.065
SMC 0.0 0.099 0.096 0.049 0.063
SMC 0.3 0.103 0.087 0.042 0.381
SMC 0.5 0.090 0.078 0.051 0.239
SMC 0.9 0.101 0.103 0.058 -0.034
SMC 0.99 0.107 0.077 0.033 0.915
Metro 0.0 4.015 0.096 0.049 80.247
Metro 0.3 4.140 0.087 0.042 96.305
Metro 0.5 4.095 0.078 0.051 79.191
Metro 0.9 4.243 0.103 0.058 71.856
Metro 0.99 4.274 0.077 0.033 128.084
DEMetro_Z 0.0 3.636 0.096 0.049 72.489
DEMetro_Z 0.3 3.392 0.087 0.042 78.539
DEMetro_Z 0.5 3.497 0.078 0.051 67.401
DEMetro_Z 0.9 4.132 0.103 0.058 69.923
DEMetro_Z 0.99 4.067 0.077 0.033 121.756
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 148.640 3.46e-39 84.937
HMC 0.3 199.585 4.43e-45 101.848
HMC 0.5 121.952 9.24e-35 81.065
HMC 0.9 135.355 5e-43 62.301
HMC 0.99 127.461 3.09e-32 118.310
SMC 0.0 -0.132 0.896 -0.045
SMC 0.3 1.253 0.218 0.451
SMC 0.5 0.772 0.445 0.247
SMC 0.9 -0.384 0.703 -0.124
SMC 0.99 1.920 0.0635 0.773
Metro 0.0 46.124 1.82e-21 82.323
Metro 0.3 107.831 1.17e-30 100.642
Metro 0.5 106.253 8.29e-32 82.333
Metro 0.9 146.222 5.22e-46 62.951
Metro 0.99 76.650 6.61e-26 124.033
DEMetro_Z 0.0 11.200 8.01e-10 71.634
DEMetro_Z 0.3 9.413 1.37e-08 81.767
DEMetro_Z 0.5 9.670 8.83e-09 66.296
DEMetro_Z 0.9 113.514 1.02e-36 62.922
DEMetro_Z 0.99 136.756 2.68e-33 119.331
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 11.008 1.1e-09 2.461
DEMetro_Z_vs_SMC 0.3 9.320 1.62e-08 2.084
DEMetro_Z_vs_SMC 0.5 9.640 9.47e-09 2.156
DEMetro_Z_vs_SMC 0.9 101.715 1.81e-27 22.744
DEMetro_Z_vs_SMC 0.99 130.064 1.7e-29 29.083
HMC_vs_Metro 0.0 1.387 0.182 0.310
HMC_vs_Metro 0.3 1.432 0.169 0.320
HMC_vs_Metro 0.5 -1.415 0.173 -0.316
HMC_vs_Metro 0.9 -1.190 0.249 -0.266
HMC_vs_Metro 0.99 -2.680 0.0148 -0.599
Metro_vs_DEMetro_Z 0.0 1.518 0.146 0.339
Metro_vs_DEMetro_Z 0.3 2.122 0.0472 0.475
Metro_vs_DEMetro_Z 0.5 2.315 0.0319 0.518
Metro_vs_DEMetro_Z 0.9 0.047 0.963 0.010
Metro_vs_DEMetro_Z 0.99 2.281 0.0343 0.510
HMC_vs_SMC 0.0 153.718 7.15e-31 34.372
HMC_vs_SMC 0.3 194.272 8.38e-33 43.441
HMC_vs_SMC 0.5 125.382 3.42e-29 28.036
HMC_vs_SMC 0.9 136.642 6.68e-30 30.554
HMC_vs_SMC 0.99 120.917 6.8e-29 27.038
Metro_vs_SMC 0.0 47.295 3.55e-21 10.576
Metro_vs_SMC 0.3 110.434 3.8e-28 24.694
Metro_vs_SMC 0.5 116.485 1.38e-28 26.047
Metro_vs_SMC 0.9 126.451 2.91e-29 28.275
Metro_vs_SMC 0.99 82.595 9.37e-26 18.469
HMC_vs_DEMetro_Z 0.0 2.114 0.0479 0.473
HMC_vs_DEMetro_Z 0.3 2.306 0.0326 0.516
HMC_vs_DEMetro_Z 0.5 2.158 0.0439 0.483
HMC_vs_DEMetro_Z 0.9 -0.967 0.345 -0.216
HMC_vs_DEMetro_Z 0.99 -0.843 0.41 -0.189
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.627 0.012 0.007 84.937
HMC 0.3 0.624 0.011 0.006 101.848
HMC 0.5 0.619 0.009 0.008 81.065
HMC 0.9 0.620 0.013 0.010 62.301
HMC 0.99 0.625 0.009 0.005 118.310
SMC 0.0 0.012 0.012 0.007 -0.045
SMC 0.3 0.014 0.011 0.006 0.451
SMC 0.5 0.011 0.009 0.008 0.247
SMC 0.9 0.012 0.013 0.010 -0.124
SMC 0.99 0.013 0.009 0.005 0.773
Metro 0.0 0.608 0.012 0.007 82.323
Metro 0.3 0.616 0.011 0.006 100.642
Metro 0.5 0.628 0.009 0.008 82.333
Metro 0.9 0.626 0.013 0.010 62.951
Metro 0.99 0.655 0.009 0.005 124.033
DEMetro_Z 0.0 0.531 0.012 0.007 71.634
DEMetro_Z 0.3 0.503 0.011 0.006 81.767
DEMetro_Z 0.5 0.508 0.009 0.008 66.296
DEMetro_Z 0.9 0.626 0.013 0.010 62.922
DEMetro_Z 0.99 0.630 0.009 0.005 119.331
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_heavy_Tails_and_high_Dimension (MvStudentT, correlation, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.547 0.137 1.482
HMC 0.3 3.837 0.00101 4.714
HMC 0.5 3.134 0.00534 6.150
HMC 0.9 3.045 0.00657 7.342
HMC 0.99 2.864 0.00991 15.004
SMC 0.0 37.427 1.16e-19 70.453
SMC 0.3 62.624 1.62e-23 427.372
SMC 0.5 37.649 2.36e-19 222.757
SMC 0.9 118.301 1.01e-28 2213.543
SMC 0.99 52.424 4.32e-22 252.879
Metro 0.0 3.803 0.00119 16.639
Metro 0.3 5.549 2.36e-05 72.919
Metro 0.5 4.951 8.84e-05 47.806
Metro 0.9 4.368 0.000331 926.552
Metro 0.99 5.328 3.84e-05 1072.032
DEMetro_Z 0.0 19.088 7.37e-14 314.853
DEMetro_Z 0.3 15.367 3.59e-12 1018.187
DEMetro_Z 0.5 7.378 5.46e-07 588.555
DEMetro_Z 0.9 10.397 2.8e-09 2940.424
DEMetro_Z 0.99 10.260 3.47e-09 489.219
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -18.961 8.38e-14 -4.240
HMC_vs_DEMetro_Z 0.3 -15.216 4.28e-12 -3.402
HMC_vs_DEMetro_Z 0.5 -7.265 6.8e-07 -1.625
HMC_vs_DEMetro_Z 0.9 -10.372 2.91e-09 -2.319
HMC_vs_DEMetro_Z 0.99 -9.550 1.1e-08 -2.135
Metro_vs_SMC 0.0 -10.623 1.97e-09 -2.375
Metro_vs_SMC 0.3 -23.424 1.77e-15 -5.238
Metro_vs_SMC 0.5 -15.805 2.19e-12 -3.534
Metro_vs_SMC 0.9 -5.887 1.14e-05 -1.316
Metro_vs_SMC 0.99 4.070 0.000653 0.910
Metro_vs_DEMetro_Z 0.0 -17.844 2.51e-13 -3.990
Metro_vs_DEMetro_Z 0.3 -13.118 5.68e-11 -2.933
Metro_vs_DEMetro_Z 0.5 -6.985 1.18e-06 -1.562
Metro_vs_DEMetro_Z 0.9 -6.305 4.73e-06 -1.410
Metro_vs_DEMetro_Z 0.99 2.750 0.0127 0.615
HMC_vs_Metro 0.0 -3.255 0.00417 -0.728
HMC_vs_Metro 0.3 -5.091 6.49e-05 -1.138
HMC_vs_Metro 0.5 -4.079 0.000639 -0.912
HMC_vs_Metro 0.9 -4.324 0.000366 -0.967
HMC_vs_Metro 0.99 -5.208 5e-05 -1.165
HMC_vs_SMC 0.0 -31.493 7.32e-18 -7.042
HMC_vs_SMC 0.3 -59.859 4.16e-23 -13.385
HMC_vs_SMC 0.5 -32.857 3.32e-18 -7.347
HMC_vs_SMC 0.9 -118.921 9.33e-29 -26.592
HMC_vs_SMC 0.99 -33.879 1.87e-18 -7.576
DEMetro_Z_vs_SMC 0.0 15.502 3.08e-12 3.466
DEMetro_Z_vs_SMC 0.3 8.838 3.7e-08 1.976
DEMetro_Z_vs_SMC 0.5 4.715 0.000151 1.054
DEMetro_Z_vs_SMC 0.9 2.595 0.0178 0.580
DEMetro_Z_vs_SMC 0.99 4.951 8.87e-05 1.107
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.101 0.068 0.022 1.482
HMC 0.3 0.177 0.067 0.023 4.714
HMC 0.5 0.196 0.067 0.021 6.150
HMC 0.9 0.286 0.049 0.032 7.342
HMC 0.99 0.723 0.053 0.045 15.004
SMC 0.0 1.617 0.068 0.022 70.453
SMC 0.3 10.003 0.067 0.023 427.372
SMC 0.5 4.746 0.067 0.021 222.757
SMC 0.9 71.715 0.049 0.032 2213.543
SMC 0.99 11.345 0.053 0.045 252.879
Metro 0.0 0.434 0.068 0.022 16.639
Metro 0.3 1.762 0.067 0.023 72.919
Metro 0.5 1.071 0.067 0.021 47.806
Metro 0.9 30.047 0.049 0.032 926.552
Metro 0.99 47.925 0.053 0.045 1072.032
DEMetro_Z 0.0 6.992 0.068 0.022 314.853
DEMetro_Z 0.3 23.738 0.067 0.023 1018.187
DEMetro_Z 0.5 12.428 0.067 0.021 588.555
DEMetro_Z 0.9 95.249 0.049 0.032 2940.424
DEMetro_Z 0.99 21.899 0.053 0.045 489.219
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.030 0.976 -0.008
HMC 0.3 0.294 0.77 0.113
HMC 0.5 0.894 0.382 0.899
HMC 0.9 0.919 0.367 0.558
HMC 0.99 1.454 0.162 15.881
SMC 0.0 138.373 1.09e-31 169.617
SMC 0.3 199.303 3.9e-33 950.310
SMC 0.5 188.891 9.97e-35 215.464
SMC 0.9 255.818 4.34e-35 3552.482
SMC 0.99 265.854 2.01e-35 2587.428
Metro 0.0 1.608 0.124 6.164
Metro 0.3 3.492 0.00244 40.131
Metro 0.5 2.706 0.0138 4.959
Metro 0.9 3.208 0.00463 695.544
Metro 0.99 4.686 0.000161 2886.543
DEMetro_Z 0.0 11.098 8.9e-10 43.308
DEMetro_Z 0.3 9.928 5.91e-09 622.821
DEMetro_Z 0.5 15.689 2.28e-12 67.583
DEMetro_Z 0.9 10.774 1.56e-09 1309.639
DEMetro_Z 0.99 11.519 5.15e-10 747.235
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -134.327 9.24e-30 -30.036
HMC_vs_SMC 0.3 -194.970 7.83e-33 -43.597
HMC_vs_SMC 0.5 -109.592 4.4e-28 -24.506
HMC_vs_SMC 0.9 -253.305 5.43e-35 -56.641
HMC_vs_SMC 0.99 -187.256 1.68e-32 -41.872
Metro_vs_DEMetro_Z 0.0 -6.901 1.4e-06 -1.543
Metro_vs_DEMetro_Z 0.3 -8.868 3.51e-08 -1.983
Metro_vs_DEMetro_Z 0.5 -13.131 5.58e-11 -2.936
Metro_vs_DEMetro_Z 0.9 -2.172 0.0427 -0.486
Metro_vs_DEMetro_Z 0.99 3.315 0.00364 0.741
HMC_vs_Metro 0.0 -1.608 0.124 -0.359
HMC_vs_Metro 0.3 -3.467 0.00258 -0.775
HMC_vs_Metro 0.5 -2.457 0.0238 -0.549
HMC_vs_Metro 0.9 -3.204 0.00467 -0.717
HMC_vs_Metro 0.99 -4.669 0.000167 -1.044
HMC_vs_DEMetro_Z 0.0 -11.074 9.93e-10 -2.476
HMC_vs_DEMetro_Z 0.3 -9.917 6.02e-09 -2.217
HMC_vs_DEMetro_Z 0.5 -16.068 1.63e-12 -3.593
HMC_vs_DEMetro_Z 0.9 -10.755 1.61e-09 -2.405
HMC_vs_DEMetro_Z 0.99 -11.149 8.88e-10 -2.493
Metro_vs_SMC 0.0 -42.622 2.52e-20 -9.531
Metro_vs_SMC 0.3 -83.403 7.8e-26 -18.649
Metro_vs_SMC 0.5 -97.180 4.3e-27 -21.730
Metro_vs_SMC 0.9 -12.751 9.24e-11 -2.851
Metro_vs_SMC 0.99 0.484 0.634 0.108
DEMetro_Z_vs_SMC 0.0 -32.150 4.98e-18 -7.189
DEMetro_Z_vs_SMC 0.3 -5.183 5.29e-05 -1.159
DEMetro_Z_vs_SMC 0.5 -30.818 1.1e-17 -6.891
DEMetro_Z_vs_SMC 0.9 -19.448 5.29e-14 -4.349
DEMetro_Z_vs_SMC 0.99 -29.575 2.36e-17 -6.613
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 8.172 8.319 17.897 -0.008
HMC 0.3 10.007 8.857 10.138 0.113
HMC 0.5 16.815 8.162 9.621 0.899
HMC 0.9 11.180 6.672 8.084 0.558
HMC 0.99 28.802 2.019 1.687 15.881
SMC 0.0 3043.966 8.319 17.897 169.617
SMC 0.3 9643.364 8.857 10.138 950.310
SMC 0.5 2081.223 8.162 9.621 215.464
SMC 0.9 28723.815 6.672 8.084 3552.482
SMC 0.99 4365.718 2.019 1.687 2587.428
Metro 0.0 118.630 8.319 17.897 6.164
Metro 0.3 415.711 8.857 10.138 40.131
Metro 0.5 55.872 8.162 9.621 4.959
Metro 0.9 5629.234 6.672 8.084 695.544
Metro 0.99 4870.176 2.019 1.687 2886.543
DEMetro_Z 0.0 783.402 8.319 17.897 43.308
DEMetro_Z 0.3 6323.186 8.857 10.138 622.821
DEMetro_Z 0.5 658.404 8.162 9.621 67.583
DEMetro_Z 0.9 10593.378 6.672 8.084 1309.639
DEMetro_Z 0.99 1262.231 2.019 1.687 747.235
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.904 9.11e-05 9.146
HMC 0.3 3.269 0.00403 16.687
HMC 0.5 4.289 0.000391 16.222
HMC 0.9 4.063 0.000656 14.861
HMC 0.99 2.881 0.00956 34.445
SMC 0.0 273.155 1.03e-35 1510.463
SMC 0.3 379.334 2.21e-38 2834.413
SMC 0.5 379.231 1.89e-38 1926.321
SMC 0.9 247.440 8.32e-35 4865.202
SMC 0.99 374.718 2.46e-38 2026.869
Metro 0.0 3.603 0.0019 72.723
Metro 0.3 8.406 7.97e-08 286.644
Metro 0.5 5.401 3.27e-05 111.729
Metro 0.9 9.099 2.36e-08 1397.449
Metro 0.99 7.915 1.96e-07 2224.237
DEMetro_Z 0.0 23.780 1.34e-15 693.506
DEMetro_Z 0.3 21.670 7.38e-15 2178.700
DEMetro_Z 0.5 20.256 2.53e-14 1120.903
DEMetro_Z 0.9 18.246 1.68e-13 3610.948
DEMetro_Z 0.99 24.516 7.63e-16 1185.336
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -18.417 1.42e-13 -4.118
Metro_vs_DEMetro_Z 0.3 -17.368 4.07e-13 -3.884
Metro_vs_DEMetro_Z 0.5 -16.048 1.67e-12 -3.588
Metro_vs_DEMetro_Z 0.9 -8.729 4.49e-08 -1.952
Metro_vs_DEMetro_Z 0.99 3.379 0.00315 0.755
DEMetro_Z_vs_SMC 0.0 -28.523 4.63e-17 -6.378
DEMetro_Z_vs_SMC 0.3 -6.472 3.34e-06 -1.447
DEMetro_Z_vs_SMC 0.5 -14.398 1.13e-11 -3.220
DEMetro_Z_vs_SMC 0.9 -6.499 3.16e-06 -1.453
DEMetro_Z_vs_SMC 0.99 -17.852 2.49e-13 -3.992
HMC_vs_DEMetro_Z 0.0 -24.130 1.02e-15 -5.396
HMC_vs_DEMetro_Z 0.3 -21.346 9.71e-15 -4.773
HMC_vs_DEMetro_Z 0.5 -19.565 4.75e-14 -4.375
HMC_vs_DEMetro_Z 0.9 -18.083 1.97e-13 -4.044
HMC_vs_DEMetro_Z 0.99 -22.878 2.73e-15 -5.116
HMC_vs_Metro 0.0 -3.138 0.00541 -0.702
HMC_vs_Metro 0.3 -7.696 2.97e-07 -1.721
HMC_vs_Metro 0.5 -4.685 0.000161 -1.048
HMC_vs_Metro 0.9 -9.024 2.68e-08 -2.018
HMC_vs_Metro 0.99 -7.744 2.71e-07 -1.732
HMC_vs_SMC 0.0 -283.280 6.49e-36 -63.343
HMC_vs_SMC 0.3 -278.638 8.88e-36 -62.305
HMC_vs_SMC 0.5 -289.765 4.22e-36 -64.793
HMC_vs_SMC 0.9 -232.006 2.88e-34 -51.878
HMC_vs_SMC 0.99 -161.808 2.7e-31 -36.181
Metro_vs_SMC 0.0 -69.753 2.3e-24 -15.597
Metro_vs_SMC 0.3 -76.076 4.45e-25 -17.011
Metro_vs_SMC 0.5 -93.696 8.59e-27 -20.951
Metro_vs_SMC 0.9 -21.902 6.07e-15 -4.897
Metro_vs_SMC 0.99 0.700 0.492 0.157
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.372 0.116 0.028 9.146
HMC 0.3 0.573 0.123 0.027 16.687
HMC 0.5 0.415 0.121 0.018 16.222
HMC 0.9 0.538 0.102 0.029 14.861
HMC 0.99 0.969 0.090 0.026 34.445
SMC 0.0 42.486 0.116 0.028 1510.463
SMC 0.3 76.542 0.123 0.027 2834.413
SMC 0.5 35.088 0.121 0.018 1926.321
SMC 0.9 142.763 0.102 0.029 4865.202
SMC 0.99 51.788 0.090 0.026 2026.869
Metro 0.0 2.156 0.116 0.028 72.723
Metro 0.3 7.851 0.123 0.027 286.644
Metro 0.5 2.149 0.121 0.018 111.729
Metro 0.9 41.079 0.102 0.029 1397.449
Metro 0.99 56.822 0.090 0.026 2224.237
DEMetro_Z 0.0 19.569 0.116 0.028 693.506
DEMetro_Z 0.3 58.863 0.123 0.027 2178.700
DEMetro_Z 0.5 20.468 0.121 0.018 1120.903
DEMetro_Z 0.9 105.985 0.102 0.029 3610.948
DEMetro_Z 0.99 30.324 0.090 0.026 1185.336
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 5.028 7.42e-05 36.515
HMC 0.3 5.403 3.24e-05 52.987
HMC 0.5 4.855 0.000109 28.942
HMC 0.9 7.044 1e-06 23.777
HMC 0.99 6.304 4.54e-06 20.887
SMC 0.0 193.589 1.17e-34 236.612
SMC 0.3 125.998 5.75e-30 228.615
SMC 0.5 185.066 1.83e-35 177.699
SMC 0.9 108.614 1.12e-29 128.330
SMC 0.99 173.956 5.33e-44 86.818
Metro 0.0 9.293 1.68e-08 119.168
Metro 0.3 29.685 2.11e-17 241.201
Metro 0.5 12.651 1.04e-10 107.251
Metro 0.9 46.399 3.97e-21 177.141
Metro 0.99 31.623 6.08e-18 163.485
DEMetro_Z 0.0 57.162 8.38e-23 277.047
DEMetro_Z 0.3 48.199 2.25e-21 295.193
DEMetro_Z 0.5 29.040 3.19e-17 249.591
DEMetro_Z 0.9 26.376 1.88e-16 188.941
DEMetro_Z 0.99 36.919 2.84e-19 125.352
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 8.596 5.67e-08 1.922
DEMetro_Z_vs_SMC 0.3 11.829 3.3e-10 2.645
DEMetro_Z_vs_SMC 0.5 8.198 1.16e-07 1.833
DEMetro_Z_vs_SMC 0.9 8.485 6.91e-08 1.897
DEMetro_Z_vs_SMC 0.99 11.597 4.6e-10 2.593
HMC_vs_Metro 0.0 -5.546 2.38e-05 -1.240
HMC_vs_Metro 0.3 -14.173 1.49e-11 -3.169
HMC_vs_Metro 0.5 -7.122 9.01e-07 -1.593
HMC_vs_Metro 0.9 -30.753 1.14e-17 -6.877
HMC_vs_Metro 0.99 -23.726 1.4e-15 -5.305
Metro_vs_DEMetro_Z 0.0 -10.441 2.61e-09 -2.335
Metro_vs_DEMetro_Z 0.3 -4.688 0.00016 -1.048
Metro_vs_DEMetro_Z 0.5 -13.029 6.38e-11 -2.913
Metro_vs_DEMetro_Z 0.9 -1.420 0.172 -0.317
Metro_vs_DEMetro_Z 0.99 6.101 7.25e-06 1.364
HMC_vs_SMC 0.0 -26.655 1.63e-16 -5.960
HMC_vs_SMC 0.3 -17.788 2.65e-13 -3.978
HMC_vs_SMC 0.5 -23.649 1.48e-15 -5.288
HMC_vs_SMC 0.9 -33.378 2.47e-18 -7.464
HMC_vs_SMC 0.99 -19.715 4.13e-14 -4.409
Metro_vs_SMC 0.0 -9.041 2.6e-08 -2.022
Metro_vs_SMC 0.3 1.481 0.155 0.331
Metro_vs_SMC 0.5 -8.468 7.14e-08 -1.893
Metro_vs_SMC 0.9 12.648 1.06e-10 2.828
Metro_vs_SMC 0.99 14.655 8.28e-12 3.277
HMC_vs_DEMetro_Z 0.0 -27.365 1e-16 -6.119
HMC_vs_DEMetro_Z 0.3 -19.578 4.69e-14 -4.378
HMC_vs_DEMetro_Z 0.5 -18.679 1.1e-13 -4.177
HMC_vs_DEMetro_Z 0.9 -23.253 2.02e-15 -5.200
HMC_vs_DEMetro_Z 0.99 -19.376 5.66e-14 -4.333
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.076 0.015 0.002 36.515
HMC 0.3 0.110 0.015 0.002 52.987
HMC 0.5 0.081 0.016 0.002 28.942
HMC 0.9 0.103 0.015 0.004 23.777
HMC 0.99 0.118 0.017 0.005 20.887
SMC 0.0 0.413 0.015 0.002 236.612
SMC 0.3 0.423 0.015 0.002 228.615
SMC 0.5 0.416 0.016 0.002 177.699
SMC 0.9 0.494 0.015 0.004 128.330
SMC 0.99 0.437 0.017 0.005 86.818
Metro 0.0 0.215 0.015 0.002 119.168
Metro 0.3 0.445 0.015 0.002 241.201
Metro 0.5 0.257 0.016 0.002 107.251
Metro 0.9 0.676 0.015 0.004 177.141
Metro 0.99 0.808 0.017 0.005 163.485
DEMetro_Z 0.0 0.481 0.015 0.002 277.047
DEMetro_Z 0.3 0.542 0.015 0.002 295.193
DEMetro_Z 0.5 0.577 0.016 0.002 249.591
DEMetro_Z 0.9 0.720 0.015 0.004 188.941
DEMetro_Z 0.99 0.624 0.017 0.005 125.352
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.005 0.0585 2.454
HMC 0.3 1.748 0.0965 7.394
HMC 0.5 3.918 0.000606 2.318
HMC 0.9 1.812 0.0858 18.499
HMC 0.99 3.893 0.000901 5.357
SMC 0.0 24.881 3.84e-16 60.708
SMC 0.3 40.330 6.86e-20 381.885
SMC 0.5 24.692 6.41e-16 184.540
SMC 0.9 52.824 4.4e-22 1955.218
SMC 0.99 31.105 8.8e-18 242.006
Metro 0.0 6.701 1.43e-06 7.772
Metro 0.3 2.892 0.00933 43.966
Metro 0.5 5.938 1.01e-05 30.451
Metro 0.9 1.902 0.0724 1996.428
Metro 0.99 4.537 0.000226 955.193
DEMetro_Z 0.0 20.857 1.47e-14 316.493
DEMetro_Z 0.3 9.926 5.93e-09 1500.214
DEMetro_Z 0.5 6.683 2.17e-06 725.778
DEMetro_Z 0.9 9.110 2.31e-08 3661.296
DEMetro_Z 0.99 7.031 1.08e-06 540.754
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -20.546 1.95e-14 -4.594
HMC_vs_DEMetro_Z 0.3 -9.836 6.87e-09 -2.199
HMC_vs_DEMetro_Z 0.5 -6.669 2.23e-06 -1.491
HMC_vs_DEMetro_Z 0.9 -9.060 2.52e-08 -2.026
HMC_vs_DEMetro_Z 0.99 -6.981 1.19e-06 -1.561
Metro_vs_SMC 0.0 -24.332 8.78e-16 -5.441
Metro_vs_SMC 0.3 -19.400 5.54e-14 -4.338
Metro_vs_SMC 0.5 -20.308 2.41e-14 -4.541
Metro_vs_SMC 0.9 0.039 0.969 0.009
Metro_vs_SMC 0.99 3.387 0.0031 0.757
Metro_vs_DEMetro_Z 0.0 -20.265 2.51e-14 -4.531
Metro_vs_DEMetro_Z 0.3 -9.714 8.38e-09 -2.172
Metro_vs_DEMetro_Z 0.5 -6.320 4.58e-06 -1.413
Metro_vs_DEMetro_Z 0.9 -1.501 0.15 -0.336
Metro_vs_DEMetro_Z 0.99 2.162 0.0436 0.483
HMC_vs_Metro 0.0 -5.244 4.62e-05 -1.173
HMC_vs_Metro 0.3 -2.221 0.0387 -0.497
HMC_vs_Metro 0.5 -5.468 2.83e-05 -1.223
HMC_vs_Metro 0.9 -1.883 0.0751 -0.421
HMC_vs_Metro 0.99 -4.514 0.000237 -1.009
HMC_vs_SMC 0.0 -29.432 2.58e-17 -6.581
HMC_vs_SMC 0.3 -36.477 4.69e-19 -8.156
HMC_vs_SMC 0.5 -24.102 1.05e-15 -5.389
HMC_vs_SMC 0.9 -46.305 5.29e-21 -10.354
HMC_vs_SMC 0.99 -29.504 2.47e-17 -6.597
DEMetro_Z_vs_SMC 0.0 17.069 5.56e-13 3.817
DEMetro_Z_vs_SMC 0.3 7.462 4.64e-07 1.668
DEMetro_Z_vs_SMC 0.5 4.952 8.85e-05 1.107
DEMetro_Z_vs_SMC 0.9 4.069 0.000654 0.910
DEMetro_Z_vs_SMC 0.99 3.826 0.00114 0.856
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.122 0.068 0.022 2.454
HMC 0.3 0.239 0.067 0.023 7.394
HMC 0.5 0.116 0.067 0.021 2.318
HMC 0.9 0.648 0.049 0.032 18.499
HMC 0.99 0.292 0.053 0.045 5.357
SMC 0.0 1.403 0.068 0.022 60.708
SMC 0.3 8.945 0.067 0.023 381.885
SMC 0.5 3.943 0.067 0.021 184.540
SMC 0.9 63.352 0.049 0.032 1955.218
SMC 0.99 10.860 0.053 0.045 242.006
Metro 0.0 0.239 0.068 0.022 7.772
Metro 0.3 1.089 0.067 0.023 43.966
Metro 0.5 0.707 0.067 0.021 30.451
Metro 0.9 64.686 0.049 0.032 1996.428
Metro 0.99 42.708 0.053 0.045 955.193
DEMetro_Z 0.0 7.028 0.068 0.022 316.493
DEMetro_Z 0.3 34.944 0.067 0.023 1500.214
DEMetro_Z 0.5 15.311 0.067 0.021 725.778
DEMetro_Z 0.9 118.588 0.049 0.032 3661.296
DEMetro_Z 0.99 24.201 0.053 0.045 540.754
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.249 0.227 4.067
HMC 0.3 0.208 0.837 0.073
HMC 0.5 0.921 0.367 0.926
HMC 0.9 -0.898 0.376 -0.237
HMC 0.99 2.289 0.0329 2.834
SMC 0.0 63.642 6.55e-24 157.582
SMC 0.3 125.131 3.2e-29 912.266
SMC 0.5 116.919 2.56e-29 214.150
SMC 0.9 180.229 3.43e-32 3634.815
SMC 0.99 196.460 6.56e-33 2752.926
Metro 0.0 1.776 0.0873 0.958
Metro 0.3 1.702 0.105 23.907
Metro 0.5 1.487 0.152 1.517
Metro 0.9 1.068 0.299 5242.567
Metro 0.99 2.136 0.0459 292.004
DEMetro_Z 0.0 7.720 2.5e-07 17.955
DEMetro_Z 0.3 11.040 1.04e-09 184.502
DEMetro_Z 0.5 9.223 1.65e-08 22.831
DEMetro_Z 0.9 9.935 5.84e-09 370.821
DEMetro_Z 0.99 5.667 1.83e-05 236.935
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -42.919 2.21e-20 -9.597
HMC_vs_SMC 0.3 -125.660 3.28e-29 -28.098
HMC_vs_SMC 0.5 -93.946 8.16e-27 -21.007
HMC_vs_SMC 0.9 -180.641 3.34e-32 -40.392
HMC_vs_SMC 0.99 -194.446 8.24e-33 -43.479
Metro_vs_DEMetro_Z 0.0 -7.476 4.52e-07 -1.672
Metro_vs_DEMetro_Z 0.3 -7.271 6.72e-07 -1.626
Metro_vs_DEMetro_Z 0.5 -7.363 5.62e-07 -1.646
Metro_vs_DEMetro_Z 0.9 0.992 0.334 0.222
Metro_vs_DEMetro_Z 0.99 0.383 0.706 0.086
HMC_vs_Metro 0.0 1.093 0.288 0.244
HMC_vs_Metro 0.3 -1.691 0.107 -0.378
HMC_vs_Metro 0.5 -1.547 0.138 -0.346
HMC_vs_Metro 0.9 -1.068 0.299 -0.239
HMC_vs_Metro 0.99 -2.113 0.0481 -0.472
HMC_vs_DEMetro_Z 0.0 -4.573 0.000208 -1.022
HMC_vs_DEMetro_Z 0.3 -10.988 1.13e-09 -2.457
HMC_vs_DEMetro_Z 0.5 -7.664 3.15e-07 -1.714
HMC_vs_DEMetro_Z 0.9 -9.932 5.87e-09 -2.221
HMC_vs_DEMetro_Z 0.99 -5.597 2.13e-05 -1.251
Metro_vs_SMC 0.0 -64.751 9.41e-24 -14.479
Metro_vs_SMC 0.3 -65.606 7.34e-24 -14.670
Metro_vs_SMC 0.5 -93.893 8.25e-27 -20.995
Metro_vs_SMC 0.9 0.328 0.747 0.073
Metro_vs_SMC 0.99 -17.673 2.98e-13 -3.952
DEMetro_Z_vs_SMC 0.0 -45.159 8.48e-21 -10.098
DEMetro_Z_vs_SMC 0.3 -41.010 5.2e-20 -9.170
DEMetro_Z_vs_SMC 0.5 -74.533 6.56e-25 -16.666
DEMetro_Z_vs_SMC 0.9 -80.190 1.64e-25 -17.931
DEMetro_Z_vs_SMC 0.99 -60.673 3.22e-23 -13.567
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 81.101 8.319 17.897 4.067
HMC 0.3 9.594 8.857 10.138 0.073
HMC 0.5 17.071 8.162 9.621 0.926
HMC 0.9 4.754 6.672 8.084 -0.237
HMC 0.99 6.798 2.019 1.687 2.834
SMC 0.0 2828.565 8.319 17.897 157.582
SMC 0.3 9257.663 8.857 10.138 912.266
SMC 0.5 2068.582 8.162 9.621 214.150
SMC 0.9 29389.373 6.672 8.084 3634.815
SMC 0.99 4644.831 2.019 1.687 2752.926
Metro 0.0 25.464 8.319 17.897 0.958
Metro 0.3 251.231 8.857 10.138 23.907
Metro 0.5 22.761 8.162 9.621 1.517
Metro 0.9 42385.939 6.672 8.084 5242.567
Metro 0.99 494.484 2.019 1.687 292.004
DEMetro_Z 0.0 329.667 8.319 17.897 17.955
DEMetro_Z 0.3 1879.389 8.857 10.138 184.502
DEMetro_Z 0.5 227.825 8.162 9.621 22.831
DEMetro_Z 0.9 3004.272 6.672 8.084 370.821
DEMetro_Z 0.99 401.610 2.019 1.687 236.935
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.737 0.0985 40.905
HMC 0.3 2.736 0.0131 16.205
HMC 0.5 7.555 2.29e-07 8.346
HMC 0.9 2.301 0.0329 19.945
HMC 0.99 7.176 7.07e-07 14.981
SMC 0.0 123.721 4.23e-29 1453.693
SMC 0.3 219.792 7.72e-34 2775.463
SMC 0.5 186.686 1.68e-32 1916.898
SMC 0.9 175.498 5.73e-32 4791.992
SMC 0.99 250.607 6.03e-35 2084.988
Metro 0.0 3.850 0.00108 32.976
Metro 0.3 2.886 0.00947 124.939
Metro 0.5 5.156 5.61e-05 56.531
Metro 0.9 2.086 0.0507 1975.351
Metro 0.99 4.514 0.000237 1367.419
DEMetro_Z 0.0 15.527 2.99e-12 436.886
DEMetro_Z 0.3 16.155 1.48e-12 1517.448
DEMetro_Z 0.5 9.621 9.77e-09 884.621
DEMetro_Z 0.9 10.593 2.06e-09 3569.333
DEMetro_Z 0.99 9.899 6.2e-09 954.946
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -13.269 4.66e-11 -2.967
Metro_vs_DEMetro_Z 0.3 -13.585 3.1e-11 -3.038
Metro_vs_DEMetro_Z 0.5 -8.671 4.97e-08 -1.939
Metro_vs_DEMetro_Z 0.9 -1.604 0.125 -0.359
Metro_vs_DEMetro_Z 0.99 1.495 0.151 0.334
DEMetro_Z_vs_SMC 0.0 -35.345 8.46e-19 -7.903
DEMetro_Z_vs_SMC 0.3 -13.929 2.01e-11 -3.115
DEMetro_Z_vs_SMC 0.5 -11.552 4.92e-10 -2.583
DEMetro_Z_vs_SMC 0.9 -3.530 0.00224 -0.789
DEMetro_Z_vs_SMC 0.99 -11.644 4.3e-10 -2.604
HMC_vs_DEMetro_Z 0.0 -12.905 7.51e-11 -2.886
HMC_vs_DEMetro_Z 0.3 -15.763 2.29e-12 -3.525
HMC_vs_DEMetro_Z 0.5 -9.541 1.12e-08 -2.133
HMC_vs_DEMetro_Z 0.9 -10.526 2.29e-09 -2.354
HMC_vs_DEMetro_Z 0.99 -9.735 8.09e-09 -2.177
HMC_vs_Metro 0.0 0.378 0.71 0.084
HMC_vs_Metro 0.3 -2.428 0.0253 -0.543
HMC_vs_Metro 0.5 -4.315 0.000374 -0.965
HMC_vs_Metro 0.9 -2.063 0.053 -0.461
HMC_vs_Metro 0.99 -4.465 0.000265 -0.998
HMC_vs_SMC 0.0 -62.129 2.06e-23 -13.893
HMC_vs_SMC 0.3 -206.039 2.74e-33 -46.072
HMC_vs_SMC 0.5 -186.668 1.79e-32 -41.740
HMC_vs_SMC 0.9 -159.688 3.47e-31 -35.707
HMC_vs_SMC 0.99 -226.819 4.42e-34 -50.718
Metro_vs_SMC 0.0 -123.858 4.31e-29 -27.696
Metro_vs_SMC 0.3 -63.725 1.27e-23 -14.249
Metro_vs_SMC 0.5 -120.844 6.88e-29 -27.022
Metro_vs_SMC 0.9 -2.984 0.00763 -0.667
Metro_vs_SMC 0.99 -2.356 0.0294 -0.527
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.263 0.116 0.028 40.905
HMC 0.3 0.560 0.123 0.027 16.205
HMC 0.5 0.272 0.121 0.018 8.346
HMC 0.9 0.687 0.102 0.029 19.945
HMC 0.99 0.472 0.090 0.026 14.981
SMC 0.0 40.893 0.116 0.028 1453.693
SMC 0.3 74.952 0.123 0.027 2775.463
SMC 0.5 34.917 0.121 0.018 1916.898
SMC 0.9 140.616 0.102 0.029 4791.992
SMC 0.99 53.270 0.090 0.026 2084.988
Metro 0.0 1.041 0.116 0.028 32.976
Metro 0.3 3.491 0.123 0.027 124.939
Metro 0.5 1.147 0.121 0.018 56.531
Metro 0.9 58.025 0.102 0.029 1975.351
Metro 0.99 34.968 0.090 0.026 1367.419
DEMetro_Z 0.0 12.371 0.116 0.028 436.886
DEMetro_Z 0.3 41.035 0.123 0.027 1517.448
DEMetro_Z 0.5 16.179 0.121 0.018 884.621
DEMetro_Z 0.9 104.764 0.102 0.029 3569.333
DEMetro_Z 0.99 24.447 0.090 0.026 954.946
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.515 0.021 45.384
HMC 0.3 2.392 0.0272 63.304
HMC 0.5 5.315 3.71e-05 12.119
HMC 0.9 2.265 0.0354 32.722
HMC 0.99 5.599 2.07e-05 21.031
SMC 0.0 189.825 2.14e-34 237.597
SMC 0.3 154.038 4.9e-32 231.790
SMC 0.5 134.967 3.27e-31 179.563
SMC 0.9 128.937 5.97e-32 128.293
SMC 0.99 92.047 6.35e-29 90.726
Metro 0.0 6.772 1.8e-06 76.173
Metro 0.3 7.786 2.49e-07 145.202
Metro 0.5 8.018 1.61e-07 89.341
Metro 0.9 36.624 4e-19 226.289
Metro 0.99 38.695 1.39e-19 213.522
DEMetro_Z 0.0 39.799 8.69e-20 326.030
DEMetro_Z 0.3 32.017 5.26e-18 371.096
DEMetro_Z 0.5 20.701 1.68e-14 304.193
DEMetro_Z 0.9 26.561 1.68e-16 230.226
DEMetro_Z 0.99 19.518 4.8e-14 153.095
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 10.816 1.47e-09 2.418
DEMetro_Z_vs_SMC 0.3 12.355 1.58e-10 2.763
DEMetro_Z_vs_SMC 0.5 8.228 1.1e-07 1.840
DEMetro_Z_vs_SMC 0.9 11.367 6.43e-10 2.542
DEMetro_Z_vs_SMC 0.99 7.615 3.46e-07 1.703
HMC_vs_Metro 0.0 -1.544 0.139 -0.345
HMC_vs_Metro 0.3 -2.229 0.0381 -0.498
HMC_vs_Metro 0.5 -6.756 1.87e-06 -1.511
HMC_vs_Metro 0.9 -11.711 3.91e-10 -2.619
HMC_vs_Metro 0.99 -29.089 3.21e-17 -6.504
Metro_vs_DEMetro_Z 0.0 -17.277 4.47e-13 -3.863
Metro_vs_DEMetro_Z 0.3 -9.829 6.95e-09 -2.198
Metro_vs_DEMetro_Z 0.5 -9.874 6.45e-09 -2.208
Metro_vs_DEMetro_Z 0.9 -0.410 0.686 -0.092
Metro_vs_DEMetro_Z 0.99 8.331 9.12e-08 1.863
HMC_vs_SMC 0.0 -10.460 2.54e-09 -2.339
HMC_vs_SMC 0.3 -6.367 4.16e-06 -1.424
HMC_vs_SMC 0.5 -55.633 1.66e-22 -12.440
HMC_vs_SMC 0.9 -6.527 2.99e-06 -1.459
HMC_vs_SMC 0.99 -17.336 4.21e-13 -3.876
Metro_vs_SMC 0.0 -13.736 2.56e-11 -3.071
Metro_vs_SMC 0.3 -4.566 0.000211 -1.021
Metro_vs_SMC 0.5 -7.734 2.76e-07 -1.729
Metro_vs_SMC 0.9 14.818 6.82e-12 3.313
Metro_vs_SMC 0.99 21.760 6.84e-15 4.866
HMC_vs_DEMetro_Z 0.0 -13.353 4.18e-11 -2.986
HMC_vs_DEMetro_Z 0.3 -9.335 1.58e-08 -2.087
HMC_vs_DEMetro_Z 0.5 -20.756 1.62e-14 -4.641
HMC_vs_DEMetro_Z 0.9 -12.146 2.11e-10 -2.716
HMC_vs_DEMetro_Z 0.99 -14.786 7.09e-12 -3.306
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.091 0.015 0.002 45.384
HMC 0.3 0.128 0.015 0.002 63.304
HMC 0.5 0.043 0.016 0.002 12.119
HMC 0.9 0.137 0.015 0.004 32.722
HMC 0.99 0.119 0.017 0.005 21.031
SMC 0.0 0.415 0.015 0.002 237.597
SMC 0.3 0.429 0.015 0.002 231.790
SMC 0.5 0.420 0.016 0.002 179.563
SMC 0.9 0.493 0.015 0.004 128.293
SMC 0.99 0.456 0.017 0.005 90.726
Metro 0.0 0.143 0.015 0.002 76.173
Metro 0.3 0.274 0.015 0.002 145.202
Metro 0.5 0.217 0.016 0.002 89.341
Metro 0.9 0.859 0.015 0.004 226.289
Metro 0.99 1.050 0.017 0.005 213.522
DEMetro_Z 0.0 0.563 0.015 0.002 326.030
DEMetro_Z 0.3 0.677 0.015 0.002 371.096
DEMetro_Z 0.5 0.700 0.016 0.002 304.193
DEMetro_Z 0.9 0.874 0.015 0.004 230.226
DEMetro_Z 0.99 0.758 0.017 0.005 153.095
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Dimension

▼

Vary_only_Dimension (MvNormal, dimension, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.560 0.579 -0.191
HMC 5 -2.410 0.0212 -0.681
HMC 10 0.478 0.635 0.154
HMC 15 -1.770 0.0849 -0.585
HMC 30 -3.698 0.000809 -1.548
SMC 2 -0.059 0.953 -0.022
SMC 5 -0.732 0.468 -0.238
SMC 10 1.185 0.244 0.438
SMC 15 0.821 0.417 0.288
SMC 30 1.059 0.297 0.420
Metro 2 1.373 0.181 0.675
Metro 5 5.202 1.06e-05 2.142
Metro 10 7.330 2.64e-08 3.121
Metro 15 9.052 1.99e-09 5.260
Metro 30 11.380 4.26e-11 7.585
DEMetro_Z 2 2.632 0.0146 1.716
DEMetro_Z 5 8.382 8.32e-08 400.100
DEMetro_Z 10 16.764 7.67e-13 1086.421
DEMetro_Z 15 25.432 3.88e-16 2086.429
DEMetro_Z 30 25.736 3.11e-16 3275.468
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.494 0.022 -0.558
HMC_vs_DEMetro_Z 1 -8.410 7.91e-08 -1.881
HMC_vs_DEMetro_Z 2 -16.744 7.83e-13 -3.744
HMC_vs_DEMetro_Z 3 -25.436 3.87e-16 -5.688
HMC_vs_DEMetro_Z 4 -25.726 3.14e-16 -5.752
Metro_vs_SMC 0 1.334 0.198 0.298
Metro_vs_SMC 1 4.844 0.000113 1.083
Metro_vs_SMC 2 9.108 2.32e-08 2.037
Metro_vs_SMC 3 8.293 9.78e-08 1.854
Metro_vs_SMC 4 10.267 3.43e-09 2.296
Metro_vs_DEMetro_Z 0 -1.355 0.191 -0.303
Metro_vs_DEMetro_Z 1 -8.347 8.87e-08 -1.866
Metro_vs_DEMetro_Z 2 -16.706 8.16e-13 -3.735
Metro_vs_DEMetro_Z 3 -25.327 4.19e-16 -5.663
Metro_vs_DEMetro_Z 4 -25.693 3.21e-16 -5.745
HMC_vs_Metro 0 -1.803 0.0873 -0.403
HMC_vs_Metro 1 -7.295 6.41e-07 -1.631
HMC_vs_Metro 2 -6.771 1.82e-06 -1.514
HMC_vs_Metro 3 -11.024 1.07e-09 -2.465
HMC_vs_Metro 4 -14.525 9.68e-12 -3.248
HMC_vs_SMC 0 -0.705 0.489 -0.158
HMC_vs_SMC 1 -2.177 0.0423 -0.487
HMC_vs_SMC 2 -0.924 0.367 -0.207
HMC_vs_SMC 3 -3.171 0.00503 -0.709
HMC_vs_SMC 4 -5.265 4.41e-05 -1.177
DEMetro_Z_vs_SMC 0 2.303 0.0328 0.515
DEMetro_Z_vs_SMC 1 8.400 8.07e-08 1.878
DEMetro_Z_vs_SMC 2 16.762 7.68e-13 3.748
DEMetro_Z_vs_SMC 3 25.448 3.84e-16 5.690
DEMetro_Z_vs_SMC 4 25.716 3.16e-16 5.750
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.020 0.022 0.010 -0.191
HMC 5 0.017 0.021 0.007 -0.681
HMC 10 0.021 0.020 0.004 0.154
HMC 15 0.020 0.022 0.003 -0.585
HMC 30 0.019 0.022 0.002 -1.548
SMC 2 0.022 0.022 0.010 -0.022
SMC 5 0.020 0.021 0.007 -0.238
SMC 10 0.022 0.020 0.004 0.438
SMC 15 0.023 0.022 0.003 0.288
SMC 30 0.023 0.022 0.002 0.420
Metro 2 0.029 0.022 0.010 0.675
Metro 5 0.036 0.021 0.007 2.142
Metro 10 0.034 0.020 0.004 3.121
Metro 15 0.037 0.022 0.003 5.260
Metro 30 0.037 0.022 0.002 7.585
DEMetro_Z 2 0.039 0.022 0.010 1.716
DEMetro_Z 5 2.737 0.021 0.007 400.100
DEMetro_Z 10 4.728 0.020 0.004 1086.421
DEMetro_Z 15 6.044 0.022 0.003 2086.429
DEMetro_Z 30 6.662 0.022 0.002 3275.468
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.927 0.36 0.333
HMC 5 1.926 0.0618 0.656
HMC 10 2.726 0.0103 1.149
HMC 15 5.439 3.82e-06 1.943
HMC 30 7.744 5.98e-09 3.096
SMC 2 -1.403 0.169 -0.400
SMC 5 0.334 0.741 0.124
SMC 10 -0.254 0.801 -0.083
SMC 15 1.670 0.103 0.538
SMC 30 3.382 0.0019 1.401
Metro 2 2.103 0.044 0.959
Metro 5 4.204 0.000239 2.072
Metro 10 7.393 5e-08 3.729
Metro 15 9.572 1.28e-10 4.366
Metro 30 14.583 2.77e-16 5.614
DEMetro_Z 2 4.893 2.59e-05 2.005
DEMetro_Z 5 8.509 6.63e-08 4485.842
DEMetro_Z 10 17.048 5.68e-13 22618.876
DEMetro_Z 15 14.972 5.69e-12 22728.928
DEMetro_Z 30 23.532 1.63e-15 42747.862
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.451 0.0241 0.548
HMC_vs_SMC 1 1.280 0.216 0.286
HMC_vs_SMC 2 2.629 0.0165 0.588
HMC_vs_SMC 3 4.624 0.000185 1.034
HMC_vs_SMC 4 3.450 0.00268 0.771
Metro_vs_DEMetro_Z 0 -2.766 0.0123 -0.618
Metro_vs_DEMetro_Z 1 -8.501 6.72e-08 -1.901
Metro_vs_DEMetro_Z 2 -17.045 5.7e-13 -3.811
Metro_vs_DEMetro_Z 3 -14.969 5.71e-12 -3.347
Metro_vs_DEMetro_Z 4 -23.528 1.63e-15 -5.261
HMC_vs_Metro 0 -1.286 0.214 -0.287
HMC_vs_Metro 1 -2.990 0.00753 -0.669
HMC_vs_Metro 2 -4.335 0.000357 -0.969
HMC_vs_Metro 3 -5.210 4.99e-05 -1.165
HMC_vs_Metro 4 -5.723 1.62e-05 -1.280
HMC_vs_DEMetro_Z 0 -3.281 0.00393 -0.734
HMC_vs_DEMetro_Z 1 -8.507 6.65e-08 -1.902
HMC_vs_DEMetro_Z 2 -17.047 5.69e-13 -3.812
HMC_vs_DEMetro_Z 3 -14.970 5.7e-12 -3.347
HMC_vs_DEMetro_Z 4 -23.530 1.63e-15 -5.261
Metro_vs_SMC 0 3.668 0.00164 0.820
Metro_vs_SMC 1 3.599 0.00191 0.805
Metro_vs_SMC 2 7.273 6.7e-07 1.626
Metro_vs_SMC 3 8.316 9.38e-08 1.860
Metro_vs_SMC 4 11.157 8.78e-10 2.495
DEMetro_Z_vs_SMC 0 7.000 1.15e-06 1.565
DEMetro_Z_vs_SMC 1 8.508 6.64e-08 1.902
DEMetro_Z_vs_SMC 2 17.048 5.68e-13 3.812
DEMetro_Z_vs_SMC 3 14.972 5.69e-12 3.348
DEMetro_Z_vs_SMC 4 23.531 1.63e-15 5.262
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.036 0.031 0.016 0.333
HMC 5 0.036 0.031 0.009 0.656
HMC 10 0.037 0.031 0.006 1.149
HMC 15 0.042 0.030 0.006 1.943
HMC 30 0.043 0.031 0.004 3.096
SMC 2 0.024 0.031 0.016 -0.400
SMC 5 0.032 0.031 0.009 0.124
SMC 10 0.030 0.031 0.006 -0.083
SMC 15 0.033 0.030 0.006 0.538
SMC 30 0.037 0.031 0.004 1.401
Metro 2 0.046 0.031 0.016 0.959
Metro 5 0.049 0.031 0.009 2.072
Metro 10 0.052 0.031 0.006 3.729
Metro 15 0.058 0.030 0.006 4.366
Metro 30 0.052 0.031 0.004 5.614
DEMetro_Z 2 0.063 0.031 0.016 2.005
DEMetro_Z 5 38.385 0.031 0.009 4485.842
DEMetro_Z 10 128.127 0.031 0.006 22618.876
DEMetro_Z 15 146.588 0.030 0.006 22728.928
DEMetro_Z 30 156.922 0.031 0.004 42747.862
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.500 0.621 -0.197
HMC 5 -0.918 0.365 -0.260
HMC 10 1.716 0.0943 0.541
HMC 15 0.905 0.371 0.310
HMC 30 0.727 0.472 0.252
SMC 2 -0.043 0.966 -0.019
SMC 5 0.577 0.567 0.172
SMC 10 1.058 0.297 0.333
SMC 15 1.175 0.248 0.411
SMC 30 2.294 0.0278 0.846
Metro 2 3.844 0.000779 2.487
Metro 5 6.920 9.08e-08 3.009
Metro 10 8.771 7.07e-10 3.862
Metro 15 11.821 1.51e-11 7.541
Metro 30 12.696 2.76e-12 7.870
DEMetro_Z 2 6.363 1.94e-06 4.944
DEMetro_Z 5 14.427 1.09e-11 879.007
DEMetro_Z 10 27.663 8.18e-17 2920.873
DEMetro_Z 15 27.443 9.48e-17 5740.503
DEMetro_Z 30 35.888 6.36e-19 7039.566
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.495 0.022 -0.558
Metro_vs_DEMetro_Z 1 -14.370 1.17e-11 -3.213
Metro_vs_DEMetro_Z 2 -27.584 8.62e-17 -6.168
Metro_vs_DEMetro_Z 3 -27.408 9.71e-17 -6.129
Metro_vs_DEMetro_Z 4 -35.861 6.45e-19 -8.019
DEMetro_Z_vs_SMC 0 5.767 1.48e-05 1.290
DEMetro_Z_vs_SMC 1 14.427 1.09e-11 3.226
DEMetro_Z_vs_SMC 2 27.641 8.3e-17 6.181
DEMetro_Z_vs_SMC 3 27.453 9.42e-17 6.139
DEMetro_Z_vs_SMC 4 35.858 6.46e-19 8.018
HMC_vs_DEMetro_Z 0 -6.383 4.02e-06 -1.427
HMC_vs_DEMetro_Z 1 -14.448 1.06e-11 -3.231
HMC_vs_DEMetro_Z 2 -27.626 8.38e-17 -6.177
HMC_vs_DEMetro_Z 3 -27.456 9.4e-17 -6.139
HMC_vs_DEMetro_Z 4 -35.861 6.45e-19 -8.019
HMC_vs_Metro 0 -4.456 0.000271 -0.996
HMC_vs_Metro 1 -8.884 3.41e-08 -1.987
HMC_vs_Metro 2 -8.376 8.42e-08 -1.873
HMC_vs_Metro 3 -11.703 3.95e-10 -2.617
HMC_vs_Metro 4 -13.077 5.99e-11 -2.924
HMC_vs_SMC 0 -0.496 0.625 -0.111
HMC_vs_SMC 1 -2.333 0.0308 -0.522
HMC_vs_SMC 2 1.101 0.284 0.246
HMC_vs_SMC 3 -0.314 0.757 -0.070
HMC_vs_SMC 4 -2.025 0.0571 -0.453
Metro_vs_SMC 0 3.613 0.00185 0.808
Metro_vs_SMC 1 6.724 2e-06 1.503
Metro_vs_SMC 2 11.078 9.87e-10 2.477
Metro_vs_SMC 3 10.479 2.46e-09 2.343
Metro_vs_SMC 4 11.487 5.4e-10 2.569
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.030 0.030 0.005 -0.197
HMC 5 0.027 0.028 0.004 -0.260
HMC 10 0.029 0.028 0.003 0.541
HMC 15 0.029 0.029 0.002 0.310
HMC 30 0.029 0.028 0.001 0.252
SMC 2 0.030 0.030 0.005 -0.019
SMC 5 0.029 0.028 0.004 0.172
SMC 10 0.029 0.028 0.003 0.333
SMC 15 0.029 0.029 0.002 0.411
SMC 30 0.030 0.028 0.001 0.846
Metro 2 0.042 0.030 0.005 2.487
Metro 5 0.041 0.028 0.004 3.009
Metro 10 0.039 0.028 0.003 3.862
Metro 15 0.041 0.029 0.002 7.541
Metro 30 0.040 0.028 0.001 7.870
DEMetro_Z 2 0.054 0.030 0.005 4.944
DEMetro_Z 5 3.881 0.028 0.004 879.007
DEMetro_Z 10 8.587 0.028 0.003 2920.873
DEMetro_Z 15 9.336 0.029 0.002 5740.503
DEMetro_Z 30 9.935 0.028 0.001 7039.566
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.454 0.652 -0.169
HMC 5 -1.058 0.297 -0.295
HMC 10 1.219 0.23 0.425
HMC 15 0.200 0.843 0.068
HMC 30 -1.262 0.215 -0.458
SMC 2 -0.439 0.663 -0.159
SMC 5 0.260 0.796 0.079
SMC 10 0.936 0.356 0.361
SMC 15 1.182 0.245 0.389
SMC 30 1.196 0.24 0.481
Metro 2 4.095 0.000331 2.077
Metro 5 6.710 9.79e-08 2.574
Metro 10 8.559 1.08e-09 3.700
Metro 15 10.170 1.97e-10 5.938
Metro 30 11.336 5.74e-11 7.883
DEMetro_Z 2 5.041 4.09e-05 3.538
DEMetro_Z 5 37.477 2.41e-19 168.500
DEMetro_Z 10 39.381 1.05e-19 289.487
DEMetro_Z 15 53.383 3.38e-22 402.136
DEMetro_Z 30 64.766 8.84e-24 554.466
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.827 0.000117 1.079
DEMetro_Z_vs_SMC 1 37.495 2.8e-19 8.384
DEMetro_Z_vs_SMC 2 39.903 8.69e-20 8.923
DEMetro_Z_vs_SMC 3 53.091 4.01e-22 11.872
DEMetro_Z_vs_SMC 4 65.354 7.9e-24 14.614
HMC_vs_Metro 0 -4.908 9.77e-05 -1.097
HMC_vs_Metro 1 -8.088 1.42e-07 -1.809
HMC_vs_Metro 2 -7.049 1.04e-06 -1.576
HMC_vs_Metro 3 -11.170 8.61e-10 -2.498
HMC_vs_Metro 4 -12.453 1.38e-10 -2.785
Metro_vs_DEMetro_Z 0 -1.738 0.0984 -0.389
Metro_vs_DEMetro_Z 1 -37.359 2.99e-19 -8.354
Metro_vs_DEMetro_Z 2 -39.516 1.04e-19 -8.836
Metro_vs_DEMetro_Z 3 -52.991 4.16e-22 -11.849
Metro_vs_DEMetro_Z 4 -63.044 1.56e-23 -14.097
HMC_vs_SMC 0 -0.034 0.973 -0.008
HMC_vs_SMC 1 -1.934 0.0681 -0.433
HMC_vs_SMC 2 0.204 0.84 0.046
HMC_vs_SMC 3 -1.015 0.323 -0.227
HMC_vs_SMC 4 -2.888 0.00942 -0.646
Metro_vs_SMC 0 4.365 0.000333 0.976
Metro_vs_SMC 1 6.268 5.11e-06 1.402
Metro_vs_SMC 2 11.731 3.8e-10 2.623
Metro_vs_SMC 3 9.070 2.48e-08 2.028
Metro_vs_SMC 4 11.214 8.07e-10 2.507
HMC_vs_DEMetro_Z 0 -5.516 2.55e-05 -1.233
HMC_vs_DEMetro_Z 1 -38.365 1.82e-19 -8.579
HMC_vs_DEMetro_Z 2 -39.941 8.54e-20 -8.931
HMC_vs_DEMetro_Z 3 -52.953 4.21e-22 -11.841
HMC_vs_DEMetro_Z 4 -65.263 8.11e-24 -14.593
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.014 0.015 0.004 -0.169
HMC 5 0.013 0.014 0.003 -0.295
HMC 10 0.014 0.013 0.002 0.425
HMC 15 0.014 0.014 0.001 0.068
HMC 30 0.014 0.014 0.001 -0.458
SMC 2 0.014 0.015 0.004 -0.159
SMC 5 0.014 0.014 0.003 0.079
SMC 10 0.014 0.013 0.002 0.361
SMC 15 0.014 0.014 0.001 0.389
SMC 30 0.015 0.014 0.001 0.481
Metro 2 0.022 0.015 0.004 2.077
Metro 5 0.022 0.014 0.003 2.574
Metro 10 0.021 0.013 0.002 3.700
Metro 15 0.022 0.014 0.001 5.938
Metro 30 0.022 0.014 0.001 7.883
DEMetro_Z 2 0.028 0.015 0.004 3.538
DEMetro_Z 5 0.580 0.014 0.003 168.500
DEMetro_Z 10 0.602 0.013 0.002 289.487
DEMetro_Z 15 0.579 0.014 0.001 402.136
DEMetro_Z 30 0.587 0.014 0.001 554.466
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.695 0.0982 -0.535
HMC 5 -1.481 0.147 -0.451
HMC 10 -0.027 0.979 -0.009
HMC 15 -2.304 0.027 -0.807
HMC 30 -3.180 0.0031 -1.213
SMC 2 -0.597 0.555 -0.235
SMC 5 -0.816 0.42 -0.228
SMC 10 -0.605 0.549 -0.212
SMC 15 -0.115 0.909 -0.053
SMC 30 0.507 0.616 0.208
Metro 2 1.496 0.146 0.734
Metro 5 5.095 1.79e-05 2.324
Metro 10 9.651 2.39e-11 3.681
Metro 15 9.850 2.74e-10 5.451
Metro 30 12.746 1.49e-12 7.382
DEMetro_Z 2 3.395 0.00209 1.713
DEMetro_Z 5 5.015 7.68e-05 204.052
DEMetro_Z 10 9.427 1.35e-08 1511.209
DEMetro_Z 15 13.948 1.96e-11 2894.908
DEMetro_Z 30 18.117 1.91e-13 5531.884
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -4.913 9.65e-05 -1.099
HMC_vs_DEMetro_Z 1 -5.028 7.47e-05 -1.124
HMC_vs_DEMetro_Z 2 -9.428 1.35e-08 -2.108
HMC_vs_DEMetro_Z 3 -13.951 1.96e-11 -3.119
HMC_vs_DEMetro_Z 4 -18.121 1.9e-13 -4.052
Metro_vs_SMC 0 1.851 0.0798 0.414
Metro_vs_SMC 1 6.296 4.82e-06 1.408
Metro_vs_SMC 2 9.756 7.83e-09 2.181
Metro_vs_SMC 3 11.618 4.46e-10 2.598
Metro_vs_SMC 4 9.471 1.25e-08 2.118
Metro_vs_DEMetro_Z 0 -1.582 0.13 -0.354
Metro_vs_DEMetro_Z 1 -4.951 8.86e-05 -1.107
Metro_vs_DEMetro_Z 2 -9.404 1.4e-08 -2.103
Metro_vs_DEMetro_Z 3 -13.921 2.03e-11 -3.113
Metro_vs_DEMetro_Z 4 -18.097 1.94e-13 -4.047
HMC_vs_Metro 0 -3.006 0.00726 -0.672
HMC_vs_Metro 1 -6.121 6.96e-06 -1.369
HMC_vs_Metro 2 -11.098 9.58e-10 -2.482
HMC_vs_Metro 3 -12.361 1.57e-10 -2.764
HMC_vs_Metro 4 -14.265 1.33e-11 -3.190
HMC_vs_SMC 0 -1.109 0.281 -0.248
HMC_vs_SMC 1 -0.808 0.429 -0.181
HMC_vs_SMC 2 0.765 0.454 0.171
HMC_vs_SMC 3 -1.875 0.0762 -0.419
HMC_vs_SMC 4 -3.574 0.00203 -0.799
DEMetro_Z_vs_SMC 0 4.131 0.000568 0.924
DEMetro_Z_vs_SMC 1 5.021 7.58e-05 1.123
DEMetro_Z_vs_SMC 2 9.430 1.34e-08 2.109
DEMetro_Z_vs_SMC 3 13.957 1.94e-11 3.121
DEMetro_Z_vs_SMC 4 18.111 1.92e-13 4.050
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.017 0.022 0.010 -0.535
HMC 5 0.018 0.021 0.007 -0.451
HMC 10 0.020 0.020 0.004 -0.009
HMC 15 0.020 0.022 0.003 -0.807
HMC 30 0.019 0.022 0.002 -1.213
SMC 2 0.020 0.022 0.010 -0.235
SMC 5 0.020 0.021 0.007 -0.228
SMC 10 0.019 0.020 0.004 -0.212
SMC 15 0.022 0.022 0.003 -0.053
SMC 30 0.022 0.022 0.002 0.208
Metro 2 0.029 0.022 0.010 0.734
Metro 5 0.037 0.021 0.007 2.324
Metro 10 0.036 0.020 0.004 3.681
Metro 15 0.038 0.022 0.003 5.451
Metro 30 0.037 0.022 0.002 7.382
DEMetro_Z 2 0.039 0.022 0.010 1.713
DEMetro_Z 5 1.406 0.021 0.007 204.052
DEMetro_Z 10 6.568 0.020 0.004 1511.209
DEMetro_Z 15 8.377 0.022 0.003 2894.908
DEMetro_Z 30 11.237 0.022 0.002 5531.884
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.040 0.968 0.014
HMC 5 2.587 0.0138 0.903
HMC 10 1.352 0.185 0.461
HMC 15 4.965 1.54e-05 1.683
HMC 30 10.853 5.78e-13 3.859
SMC 2 -0.227 0.821 -0.069
SMC 5 -1.302 0.201 -0.380
SMC 10 -0.657 0.515 -0.214
SMC 15 2.051 0.0477 0.577
SMC 30 -0.557 0.581 -0.210
Metro 2 1.882 0.069 0.798
Metro 5 4.053 0.000407 2.261
Metro 10 6.639 4.4e-07 3.598
Metro 15 8.752 3.41e-10 3.452
Metro 30 12.163 1.06e-12 6.050
DEMetro_Z 2 3.167 0.00329 1.263
DEMetro_Z 5 3.358 0.00331 1626.274
DEMetro_Z 10 6.680 2.19e-06 4194.707
DEMetro_Z 15 11.746 3.72e-10 3256.878
DEMetro_Z 30 13.257 4.73e-11 6365.104
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.309 0.761 0.069
HMC_vs_SMC 1 4.165 0.000526 0.931
HMC_vs_SMC 2 1.931 0.0685 0.432
HMC_vs_SMC 3 4.066 0.000659 0.909
HMC_vs_SMC 4 9.433 1.34e-08 2.109
Metro_vs_DEMetro_Z 0 -0.780 0.445 -0.174
Metro_vs_DEMetro_Z 1 -3.354 0.00333 -0.750
Metro_vs_DEMetro_Z 2 -6.675 2.21e-06 -1.493
Metro_vs_DEMetro_Z 3 -11.732 3.79e-10 -2.623
Metro_vs_DEMetro_Z 4 -13.249 4.78e-11 -2.962
HMC_vs_Metro 0 -1.925 0.0694 -0.430
HMC_vs_Metro 1 -2.358 0.0293 -0.527
HMC_vs_Metro 2 -6.085 7.49e-06 -1.361
HMC_vs_Metro 3 -4.432 0.000286 -0.991
HMC_vs_Metro 4 -4.496 0.000247 -1.005
HMC_vs_DEMetro_Z 0 -2.984 0.00763 -0.667
HMC_vs_DEMetro_Z 1 -3.357 0.00331 -0.751
HMC_vs_DEMetro_Z 2 -6.679 2.19e-06 -1.493
HMC_vs_DEMetro_Z 3 -11.738 3.76e-10 -2.625
HMC_vs_DEMetro_Z 4 -13.251 4.77e-11 -2.963
Metro_vs_SMC 0 2.209 0.0396 0.494
Metro_vs_SMC 1 5.761 1.5e-05 1.288
Metro_vs_SMC 2 9.031 2.65e-08 2.019
Metro_vs_SMC 3 7.558 3.86e-07 1.690
Metro_vs_SMC 4 11.070 9.99e-10 2.475
DEMetro_Z_vs_SMC 0 3.821 0.00115 0.854
DEMetro_Z_vs_SMC 1 3.359 0.0033 0.751
DEMetro_Z_vs_SMC 2 6.681 2.18e-06 1.494
DEMetro_Z_vs_SMC 3 11.744 3.73e-10 2.626
DEMetro_Z_vs_SMC 4 13.257 4.73e-11 2.964
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.031 0.031 0.016 0.014
HMC 5 0.039 0.031 0.009 0.903
HMC 10 0.033 0.031 0.006 0.461
HMC 15 0.041 0.030 0.006 1.683
HMC 30 0.046 0.031 0.004 3.859
SMC 2 0.030 0.031 0.016 -0.069
SMC 5 0.028 0.031 0.009 -0.380
SMC 10 0.029 0.031 0.006 -0.214
SMC 15 0.033 0.030 0.006 0.577
SMC 30 0.031 0.031 0.004 -0.210
Metro 2 0.043 0.031 0.016 0.798
Metro 5 0.050 0.031 0.009 2.261
Metro 10 0.051 0.031 0.006 3.598
Metro 15 0.052 0.030 0.006 3.452
Metro 30 0.054 0.031 0.004 6.050
DEMetro_Z 2 0.051 0.031 0.016 1.263
DEMetro_Z 5 13.936 0.031 0.009 1626.274
DEMetro_Z 10 23.786 0.031 0.006 4194.707
DEMetro_Z 15 21.030 0.030 0.006 3256.878
DEMetro_Z 30 23.392 0.031 0.004 6365.104
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.883 0.0675 -0.640
HMC 5 0.538 0.594 0.159
HMC 10 1.704 0.0967 0.507
HMC 15 0.446 0.658 0.164
HMC 30 1.665 0.104 0.559
SMC 2 -0.309 0.759 -0.162
SMC 5 -0.424 0.674 -0.122
SMC 10 -0.397 0.694 -0.125
SMC 15 -0.140 0.89 -0.068
SMC 30 0.785 0.438 0.279
Metro 2 3.318 0.00294 2.269
Metro 5 6.498 6.63e-07 3.578
Metro 10 10.114 1.13e-11 4.058
Metro 15 10.937 1.2e-10 7.655
Metro 30 13.335 5.76e-13 7.773
DEMetro_Z 2 5.581 1.17e-05 4.167
DEMetro_Z 5 4.779 0.00013 283.342
DEMetro_Z 10 9.537 1.12e-08 1960.023
DEMetro_Z 15 14.148 1.53e-11 4453.952
DEMetro_Z 30 18.434 1.39e-13 6718.672
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.020 0.0577 -0.452
Metro_vs_DEMetro_Z 1 -4.715 0.000151 -1.054
Metro_vs_DEMetro_Z 2 -9.517 1.16e-08 -2.128
Metro_vs_DEMetro_Z 3 -14.124 1.58e-11 -3.158
Metro_vs_DEMetro_Z 4 -18.415 1.42e-13 -4.118
DEMetro_Z_vs_SMC 0 5.730 1.6e-05 1.281
DEMetro_Z_vs_SMC 1 4.780 0.00013 1.069
DEMetro_Z_vs_SMC 2 9.540 1.12e-08 2.133
DEMetro_Z_vs_SMC 3 14.157 1.52e-11 3.166
DEMetro_Z_vs_SMC 4 18.428 1.4e-13 4.121
HMC_vs_DEMetro_Z 0 -6.896 1.41e-06 -1.542
HMC_vs_DEMetro_Z 1 -4.777 0.000131 -1.068
HMC_vs_DEMetro_Z 2 -9.536 1.13e-08 -2.132
HMC_vs_DEMetro_Z 3 -14.145 1.54e-11 -3.163
HMC_vs_DEMetro_Z 4 -18.430 1.4e-13 -4.121
HMC_vs_Metro 0 -4.208 0.000476 -0.941
HMC_vs_Metro 1 -6.236 5.46e-06 -1.394
HMC_vs_Metro 2 -11.519 5.16e-10 -2.576
HMC_vs_Metro 3 -10.516 2.33e-09 -2.351
HMC_vs_Metro 4 -11.428 5.89e-10 -2.555
HMC_vs_SMC 0 -1.232 0.233 -0.276
HMC_vs_SMC 1 0.985 0.337 0.220
HMC_vs_SMC 2 2.856 0.0101 0.639
HMC_vs_SMC 3 0.462 0.649 0.103
HMC_vs_SMC 4 0.921 0.368 0.206
Metro_vs_SMC 0 3.123 0.0056 0.698
Metro_vs_SMC 1 7.291 6.47e-07 1.630
Metro_vs_SMC 2 12.290 1.73e-10 2.748
Metro_vs_SMC 3 12.665 1.04e-10 2.832
Metro_vs_SMC 4 10.644 1.91e-09 2.380
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.027 0.030 0.005 -0.640
HMC 5 0.029 0.028 0.004 0.159
HMC 10 0.029 0.028 0.003 0.507
HMC 15 0.029 0.029 0.002 0.164
HMC 30 0.029 0.028 0.001 0.559
SMC 2 0.030 0.030 0.005 -0.162
SMC 5 0.028 0.028 0.004 -0.122
SMC 10 0.027 0.028 0.003 -0.125
SMC 15 0.028 0.029 0.002 -0.068
SMC 30 0.029 0.028 0.001 0.279
Metro 2 0.041 0.030 0.005 2.269
Metro 5 0.044 0.028 0.004 3.578
Metro 10 0.040 0.028 0.003 4.058
Metro 15 0.041 0.029 0.002 7.655
Metro 30 0.039 0.028 0.001 7.773
DEMetro_Z 2 0.051 0.030 0.005 4.167
DEMetro_Z 5 1.270 0.028 0.004 283.342
DEMetro_Z 10 5.772 0.028 0.003 1960.023
DEMetro_Z 15 7.250 0.029 0.002 4453.952
DEMetro_Z 30 9.483 0.028 0.001 6718.672
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.158 0.254 -0.373
HMC 5 -0.095 0.925 -0.027
HMC 10 1.073 0.29 0.355
HMC 15 -0.320 0.751 -0.114
HMC 30 -0.298 0.768 -0.113
SMC 2 -0.378 0.708 -0.175
SMC 5 -0.845 0.403 -0.239
SMC 10 -0.274 0.786 -0.099
SMC 15 -0.125 0.901 -0.059
SMC 30 0.365 0.717 0.140
Metro 2 3.069 0.00494 1.681
Metro 5 5.599 5.19e-06 2.742
Metro 10 10.402 5.82e-12 4.197
Metro 15 11.227 1.55e-11 6.145
Metro 30 12.786 2.43e-12 7.954
DEMetro_Z 2 4.444 0.000171 2.902
DEMetro_Z 5 8.922 3.14e-08 62.706
DEMetro_Z 10 19.456 5.23e-14 390.316
DEMetro_Z 15 97.343 3.68e-27 618.023
DEMetro_Z 30 39.727 9.39e-20 914.123
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.443 0.000279 0.994
DEMetro_Z_vs_SMC 1 8.938 3.11e-08 1.999
DEMetro_Z_vs_SMC 2 19.505 5.02e-14 4.361
DEMetro_Z_vs_SMC 3 97.764 3.84e-27 21.861
DEMetro_Z_vs_SMC 4 39.616 9.96e-20 8.858
HMC_vs_Metro 0 -3.787 0.00125 -0.847
HMC_vs_Metro 1 -5.939 1.02e-05 -1.328
HMC_vs_Metro 2 -11.479 5.46e-10 -2.567
HMC_vs_Metro 3 -12.210 1.93e-10 -2.730
HMC_vs_Metro 4 -13.105 5.77e-11 -2.930
Metro_vs_DEMetro_Z 0 -1.582 0.13 -0.354
Metro_vs_DEMetro_Z 1 -8.354 8.76e-08 -1.868
Metro_vs_DEMetro_Z 2 -19.162 6.92e-14 -4.285
Metro_vs_DEMetro_Z 3 -92.955 9.98e-27 -20.785
Metro_vs_DEMetro_Z 4 -39.777 9.23e-20 -8.894
HMC_vs_SMC 0 -0.579 0.569 -0.129
HMC_vs_SMC 1 0.783 0.443 0.175
HMC_vs_SMC 2 1.643 0.117 0.367
HMC_vs_SMC 3 -0.126 0.901 -0.028
HMC_vs_SMC 4 -0.714 0.484 -0.160
Metro_vs_SMC 0 2.846 0.0103 0.636
Metro_vs_SMC 1 6.672 2.22e-06 1.492
Metro_vs_SMC 2 11.013 1.09e-09 2.463
Metro_vs_SMC 3 13.261 4.71e-11 2.965
Metro_vs_SMC 4 10.448 2.58e-09 2.336
HMC_vs_DEMetro_Z 0 -5.245 4.61e-05 -1.173
HMC_vs_DEMetro_Z 1 -8.960 2.99e-08 -2.004
HMC_vs_DEMetro_Z 2 -19.379 5.65e-14 -4.333
HMC_vs_DEMetro_Z 3 -97.336 4.17e-27 -21.765
HMC_vs_DEMetro_Z 4 -39.664 9.74e-20 -8.869
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.013 0.015 0.004 -0.373
HMC 5 0.014 0.014 0.003 -0.027
HMC 10 0.014 0.013 0.002 0.355
HMC 15 0.014 0.014 0.001 -0.114
HMC 30 0.014 0.014 0.001 -0.113
SMC 2 0.014 0.015 0.004 -0.175
SMC 5 0.013 0.014 0.003 -0.239
SMC 10 0.013 0.013 0.002 -0.099
SMC 15 0.014 0.014 0.001 -0.059
SMC 30 0.014 0.014 0.001 0.140
Metro 2 0.021 0.015 0.004 1.681
Metro 5 0.023 0.014 0.003 2.742
Metro 10 0.022 0.013 0.002 4.197
Metro 15 0.023 0.014 0.001 6.145
Metro 30 0.022 0.014 0.001 7.954
DEMetro_Z 2 0.025 0.015 0.004 2.902
DEMetro_Z 5 0.225 0.014 0.003 62.706
DEMetro_Z 10 0.807 0.013 0.002 390.316
DEMetro_Z 15 0.882 0.014 0.001 618.023
DEMetro_Z 30 0.959 0.014 0.001 914.123
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_high_correlation (MvNormal, dimension, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.327 0.195 0.636
HMC 5 1.959 0.0609 1.087
HMC 10 4.428 0.0002 3.341
HMC 15 2.416 0.0239 1.668
HMC 30 4.535 0.000195 5.534
SMC 2 -0.636 0.528 -0.224
SMC 5 -0.087 0.931 -0.029
SMC 10 2.065 0.0459 0.696
SMC 15 -0.325 0.747 -0.111
SMC 30 -1.992 0.0546 -0.538
Metro 2 4.734 0.000103 4.014
Metro 5 6.903 1.32e-06 21.813
Metro 10 4.479 0.000254 18.473
Metro 15 5.128 5.89e-05 23.742
Metro 30 4.909 9.64e-05 24.075
DEMetro_Z 2 2.966 0.00628 1.588
DEMetro_Z 5 9.044 2.59e-08 710.197
DEMetro_Z 10 16.089 1.59e-12 584.626
DEMetro_Z 15 26.746 1.52e-16 558.223
DEMetro_Z 30 31.546 7.02e-18 527.068
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.685 0.108 -0.377
HMC_vs_DEMetro_Z 1 -9.026 2.67e-08 -2.018
HMC_vs_DEMetro_Z 2 -16.021 1.72e-12 -3.582
HMC_vs_DEMetro_Z 3 -26.888 1.38e-16 -6.012
HMC_vs_DEMetro_Z 4 -30.762 1.13e-17 -6.879
Metro_vs_SMC 0 5.049 7.13e-05 1.129
Metro_vs_SMC 1 6.962 1.24e-06 1.557
Metro_vs_SMC 2 4.361 0.000336 0.975
Metro_vs_SMC 3 5.233 4.74e-05 1.170
Metro_vs_SMC 4 5.080 6.66e-05 1.136
Metro_vs_DEMetro_Z 0 2.316 0.0319 0.518
Metro_vs_DEMetro_Z 1 -8.847 3.65e-08 -1.978
Metro_vs_DEMetro_Z 2 -15.692 2.48e-12 -3.509
Metro_vs_DEMetro_Z 3 -25.278 4.34e-16 -5.652
Metro_vs_DEMetro_Z 4 -28.179 5.8e-17 -6.301
HMC_vs_Metro 0 -4.013 0.000744 -0.897
HMC_vs_Metro 1 -6.436 3.6e-06 -1.439
HMC_vs_Metro 2 -3.577 0.00201 -0.800
HMC_vs_Metro 3 -4.634 0.000181 -1.036
HMC_vs_Metro 4 -3.552 0.00213 -0.794
HMC_vs_SMC 0 1.567 0.134 0.350
HMC_vs_SMC 1 2.296 0.0332 0.513
HMC_vs_SMC 2 3.630 0.00178 0.812
HMC_vs_SMC 3 2.373 0.0284 0.531
HMC_vs_SMC 4 5.096 6.41e-05 1.140
DEMetro_Z_vs_SMC 0 3.261 0.00411 0.729
DEMetro_Z_vs_SMC 1 9.047 2.57e-08 2.023
DEMetro_Z_vs_SMC 2 16.044 1.68e-12 3.588
DEMetro_Z_vs_SMC 3 26.753 1.52e-16 5.982
DEMetro_Z_vs_SMC 4 31.556 7.05e-18 7.056
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.030 0.022 0.013 0.636
HMC 5 0.031 0.019 0.011 1.087
HMC 10 0.050 0.016 0.010 3.341
HMC 15 0.039 0.020 0.011 1.668
HMC 30 0.094 0.022 0.013 5.534
SMC 2 0.019 0.022 0.013 -0.224
SMC 5 0.019 0.019 0.011 -0.029
SMC 10 0.023 0.016 0.010 0.696
SMC 15 0.019 0.020 0.011 -0.111
SMC 30 0.015 0.022 0.013 -0.538
Metro 2 0.074 0.022 0.013 4.014
Metro 5 0.254 0.019 0.011 21.813
Metro 10 0.200 0.016 0.010 18.473
Metro 15 0.279 0.020 0.011 23.742
Metro 30 0.336 0.022 0.013 24.075
DEMetro_Z 2 0.043 0.022 0.013 1.588
DEMetro_Z 5 7.668 0.019 0.011 710.197
DEMetro_Z 10 5.834 0.016 0.010 584.626
DEMetro_Z 15 6.101 0.020 0.011 558.223
DEMetro_Z 30 6.888 0.022 0.013 527.068
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.901 0.00731 1.517
HMC 5 4.218 0.000371 3.835
HMC 10 2.975 0.00694 2.378
HMC 15 4.143 0.000396 3.013
HMC 30 3.645 0.0016 4.842
SMC 2 1.829 0.0761 0.696
SMC 5 1.601 0.12 0.707
SMC 10 0.808 0.425 0.368
SMC 15 -0.155 0.877 -0.050
SMC 30 1.728 0.0934 0.714
Metro 2 5.976 5.12e-06 4.901
Metro 5 4.504 0.000234 10.804
Metro 10 4.420 0.000291 20.475
Metro 15 6.811 1.25e-06 9.267
Metro 30 5.913 1.04e-05 20.353
DEMetro_Z 2 3.079 0.00534 2.278
DEMetro_Z 5 6.250 5.31e-06 11979.745
DEMetro_Z 10 16.936 6.39e-13 17277.565
DEMetro_Z 15 19.392 5.58e-14 10967.145
DEMetro_Z 30 31.112 9.19e-18 13017.017
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.318 0.203 0.295
HMC_vs_SMC 1 3.181 0.00492 0.711
HMC_vs_SMC 2 2.217 0.039 0.496
HMC_vs_SMC 3 3.933 0.000893 0.879
HMC_vs_SMC 4 3.276 0.00397 0.733
Metro_vs_DEMetro_Z 0 2.616 0.017 0.585
Metro_vs_DEMetro_Z 1 -6.243 5.38e-06 -1.396
Metro_vs_DEMetro_Z 2 -16.926 6.46e-13 -3.785
Metro_vs_DEMetro_Z 3 -19.374 5.67e-14 -4.332
Metro_vs_DEMetro_Z 4 -31.037 9.6e-18 -6.940
HMC_vs_Metro 0 -4.598 0.000196 -1.028
HMC_vs_Metro 1 -2.883 0.00952 -0.645
HMC_vs_Metro 2 -3.835 0.00112 -0.858
HMC_vs_Metro 3 -3.649 0.00171 -0.816
HMC_vs_Metro 4 -4.516 0.000237 -1.010
HMC_vs_DEMetro_Z 0 -0.861 0.4 -0.193
HMC_vs_DEMetro_Z 1 -6.247 5.34e-06 -1.397
HMC_vs_DEMetro_Z 2 -16.932 6.42e-13 -3.786
HMC_vs_DEMetro_Z 3 -19.395 5.56e-14 -4.337
HMC_vs_DEMetro_Z 4 -31.126 9.1e-18 -6.960
Metro_vs_SMC 0 4.981 8.3e-05 1.114
Metro_vs_SMC 1 4.372 0.000328 0.978
Metro_vs_SMC 2 4.373 0.000327 0.978
Metro_vs_SMC 3 7.584 3.67e-07 1.696
Metro_vs_SMC 4 5.537 2.43e-05 1.238
DEMetro_Z_vs_SMC 0 2.018 0.058 0.451
DEMetro_Z_vs_SMC 1 6.250 5.31e-06 1.397
DEMetro_Z_vs_SMC 2 16.934 6.41e-13 3.786
DEMetro_Z_vs_SMC 3 19.390 5.59e-14 4.336
DEMetro_Z_vs_SMC 4 31.116 9.16e-18 6.958
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.035 0.019 0.010 1.517
HMC 5 0.056 0.022 0.009 3.835
HMC 10 0.045 0.024 0.009 2.378
HMC 15 0.069 0.024 0.015 3.013
HMC 30 0.089 0.025 0.013 4.842
SMC 2 0.027 0.019 0.010 0.696
SMC 5 0.028 0.022 0.009 0.707
SMC 10 0.028 0.024 0.009 0.368
SMC 15 0.023 0.024 0.015 -0.050
SMC 30 0.035 0.025 0.013 0.714
Metro 2 0.070 0.019 0.010 4.901
Metro 5 0.119 0.022 0.009 10.804
Metro 10 0.206 0.024 0.009 20.475
Metro 15 0.161 0.024 0.015 9.267
Metro 30 0.292 0.025 0.013 20.353
DEMetro_Z 2 0.043 0.019 0.010 2.278
DEMetro_Z 5 107.500 0.022 0.009 11979.745
DEMetro_Z 10 153.178 0.024 0.009 17277.565
DEMetro_Z 15 161.695 0.024 0.015 10967.145
DEMetro_Z 30 170.473 0.025 0.013 13017.017
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.086 0.0465 1.086
HMC 5 2.873 0.00853 2.001
HMC 10 5.268 3.11e-05 5.050
HMC 15 5.720 8.87e-06 4.476
HMC 30 5.684 1.54e-05 9.382
SMC 2 -0.339 0.737 -0.124
SMC 5 0.339 0.737 0.123
SMC 10 2.474 0.0181 0.867
SMC 15 0.229 0.82 0.077
SMC 30 -1.414 0.166 -0.393
Metro 2 6.403 2.31e-06 6.151
Metro 5 7.525 3.95e-07 30.896
Metro 10 5.712 1.64e-05 32.081
Metro 15 5.880 1.15e-05 37.554
Metro 30 5.840 1.25e-05 40.175
DEMetro_Z 2 4.451 0.000151 2.603
DEMetro_Z 5 13.675 2.77e-11 1477.212
DEMetro_Z 10 32.791 3.44e-18 1822.046
DEMetro_Z 15 41.209 4.74e-20 1708.885
DEMetro_Z 30 68.535 3.18e-24 1500.886
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 3.019 0.00706 0.675
Metro_vs_DEMetro_Z 1 -13.384 4.01e-11 -2.993
Metro_vs_DEMetro_Z 2 -32.416 4.27e-18 -7.248
Metro_vs_DEMetro_Z 3 -40.061 8.07e-20 -8.958
Metro_vs_DEMetro_Z 4 -60.892 3.01e-23 -13.616
DEMetro_Z_vs_SMC 0 4.281 0.000403 0.957
DEMetro_Z_vs_SMC 1 13.684 2.74e-11 3.060
DEMetro_Z_vs_SMC 2 32.702 3.62e-18 7.312
DEMetro_Z_vs_SMC 3 41.307 4.54e-20 9.237
DEMetro_Z_vs_SMC 4 68.629 3.13e-24 15.346
HMC_vs_DEMetro_Z 0 -2.215 0.0392 -0.495
HMC_vs_DEMetro_Z 1 -13.656 2.84e-11 -3.053
HMC_vs_DEMetro_Z 2 -32.711 3.6e-18 -7.314
HMC_vs_DEMetro_Z 3 -41.213 4.74e-20 -9.216
HMC_vs_DEMetro_Z 4 -69.649 2.37e-24 -15.574
HMC_vs_Metro 0 -5.015 7.69e-05 -1.121
HMC_vs_Metro 1 -6.884 1.45e-06 -1.539
HMC_vs_Metro 2 -4.714 0.000151 -1.054
HMC_vs_Metro 3 -5.035 7.35e-05 -1.126
HMC_vs_Metro 4 -4.299 0.000387 -0.961
HMC_vs_SMC 0 2.009 0.0589 0.449
HMC_vs_SMC 1 2.902 0.00914 0.649
HMC_vs_SMC 2 4.389 0.000316 0.981
HMC_vs_SMC 3 5.370 3.51e-05 1.201
HMC_vs_SMC 4 5.870 1.18e-05 1.313
Metro_vs_SMC 0 6.520 3.03e-06 1.458
Metro_vs_SMC 1 7.485 4.44e-07 1.674
Metro_vs_SMC 2 5.621 2.02e-05 1.257
Metro_vs_SMC 3 5.925 1.05e-05 1.325
Metro_vs_SMC 4 5.920 1.06e-05 1.324
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.038 0.029 0.008 1.086
HMC 5 0.037 0.025 0.006 2.001
HMC 10 0.049 0.022 0.005 5.050
HMC 15 0.050 0.024 0.006 4.476
HMC 30 0.091 0.026 0.007 9.382
SMC 2 0.028 0.029 0.008 -0.124
SMC 5 0.025 0.025 0.006 0.123
SMC 10 0.027 0.022 0.005 0.867
SMC 15 0.025 0.024 0.006 0.077
SMC 30 0.023 0.026 0.007 -0.393
Metro 2 0.080 0.029 0.008 6.151
Metro 5 0.220 0.025 0.006 30.896
Metro 10 0.191 0.022 0.005 32.081
Metro 15 0.243 0.024 0.006 37.554
Metro 30 0.304 0.026 0.007 40.175
DEMetro_Z 2 0.050 0.029 0.008 2.603
DEMetro_Z 5 9.391 0.025 0.006 1477.212
DEMetro_Z 10 9.632 0.022 0.005 1822.046
DEMetro_Z 15 9.963 0.024 0.006 1708.885
DEMetro_Z 30 10.431 0.026 0.007 1500.886
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.485 0.148 0.689
HMC 5 3.188 0.00373 1.805
HMC 10 5.059 5.12e-05 4.887
HMC 15 6.228 1.65e-06 3.749
HMC 30 5.877 9.55e-06 8.320
SMC 2 -1.024 0.312 -0.328
SMC 5 0.525 0.603 0.188
SMC 10 2.012 0.052 0.762
SMC 15 0.250 0.804 0.080
SMC 30 -0.930 0.358 -0.288
Metro 2 6.796 8.42e-07 5.846
Metro 5 7.896 1.87e-07 22.498
Metro 10 5.878 1.15e-05 32.009
Metro 15 6.074 7.55e-06 30.466
Metro 30 7.891 1.99e-07 36.478
DEMetro_Z 2 3.877 0.000659 2.233
DEMetro_Z 5 33.619 1.88e-18 156.684
DEMetro_Z 10 39.522 8.87e-20 179.646
DEMetro_Z 15 77.349 6.22e-26 129.445
DEMetro_Z 30 70.206 4.83e-25 123.378
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.285 0.0004 0.958
DEMetro_Z_vs_SMC 1 33.939 1.81e-18 7.589
DEMetro_Z_vs_SMC 2 39.585 1.01e-19 8.851
DEMetro_Z_vs_SMC 3 74.565 6.51e-25 16.673
DEMetro_Z_vs_SMC 4 70.595 1.83e-24 15.785
HMC_vs_Metro 0 -6.012 8.75e-06 -1.344
HMC_vs_Metro 1 -6.861 1.52e-06 -1.534
HMC_vs_Metro 2 -4.832 0.000116 -1.081
HMC_vs_Metro 3 -5.223 4.84e-05 -1.168
HMC_vs_Metro 4 -5.887 1.14e-05 -1.316
Metro_vs_DEMetro_Z 0 3.557 0.0021 0.795
Metro_vs_DEMetro_Z 1 -25.085 5e-16 -5.609
Metro_vs_DEMetro_Z 2 -25.958 2.66e-16 -5.804
Metro_vs_DEMetro_Z 3 -18.386 1.46e-13 -4.111
Metro_vs_DEMetro_Z 4 -15.927 1.91e-12 -3.561
HMC_vs_SMC 0 2.026 0.0571 0.453
HMC_vs_SMC 1 3.028 0.00692 0.677
HMC_vs_SMC 2 4.565 0.000211 1.021
HMC_vs_SMC 3 5.989 9.2e-06 1.339
HMC_vs_SMC 4 5.999 8.99e-06 1.341
Metro_vs_SMC 0 6.929 1.32e-06 1.549
Metro_vs_SMC 1 7.787 2.5e-07 1.741
Metro_vs_SMC 2 5.813 1.34e-05 1.300
Metro_vs_SMC 3 6.118 6.99e-06 1.368
Metro_vs_SMC 4 7.925 1.93e-07 1.772
HMC_vs_DEMetro_Z 0 -2.176 0.0424 -0.486
HMC_vs_DEMetro_Z 1 -33.491 2.32e-18 -7.489
HMC_vs_DEMetro_Z 2 -36.291 5.16e-19 -8.115
HMC_vs_DEMetro_Z 3 -67.311 4.52e-24 -15.051
HMC_vs_DEMetro_Z 4 -45.772 6.58e-21 -10.235
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.019 0.015 0.005 0.689
HMC 5 0.022 0.013 0.005 1.805
HMC 10 0.028 0.012 0.003 4.887
HMC 15 0.030 0.014 0.004 3.749
HMC 30 0.053 0.015 0.005 8.320
SMC 2 0.014 0.015 0.005 -0.328
SMC 5 0.014 0.013 0.005 0.188
SMC 10 0.014 0.012 0.003 0.762
SMC 15 0.014 0.014 0.004 0.080
SMC 30 0.014 0.015 0.005 -0.288
Metro 2 0.044 0.015 0.005 5.846
Metro 5 0.122 0.013 0.005 22.498
Metro 10 0.120 0.012 0.003 32.009
Metro 15 0.148 0.014 0.004 30.466
Metro 30 0.182 0.015 0.005 36.478
DEMetro_Z 2 0.026 0.015 0.005 2.233
DEMetro_Z 5 0.770 0.013 0.005 156.684
DEMetro_Z 10 0.620 0.012 0.003 179.646
DEMetro_Z 15 0.582 0.014 0.004 129.445
DEMetro_Z 30 0.581 0.015 0.005 123.378
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.360 0.721 0.144
HMC 5 2.317 0.0294 1.513
HMC 10 3.164 0.00439 2.389
HMC 15 3.521 0.00196 3.066
HMC 30 6.014 5.44e-06 5.668
SMC 2 0.330 0.744 0.117
SMC 5 0.009 0.993 0.003
SMC 10 0.716 0.478 0.241
SMC 15 0.088 0.931 0.031
SMC 30 -2.003 0.0539 -0.522
Metro 2 4.994 5.79e-05 4.598
Metro 5 6.198 5.44e-06 14.256
Metro 10 5.056 6.86e-05 18.420
Metro 15 7.136 8.52e-07 33.000
Metro 30 10.013 4.63e-09 30.448
DEMetro_Z 2 2.359 0.0263 1.381
DEMetro_Z 5 4.055 0.000676 320.043
DEMetro_Z 10 11.741 3.74e-10 807.819
DEMetro_Z 15 22.906 2.66e-15 945.326
DEMetro_Z 30 38.969 1.35e-19 915.814
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.157 0.044 -0.482
HMC_vs_DEMetro_Z 1 -4.035 0.000707 -0.902
HMC_vs_DEMetro_Z 2 -11.691 4.02e-10 -2.614
HMC_vs_DEMetro_Z 3 -23.006 2.46e-15 -5.144
HMC_vs_DEMetro_Z 4 -38.568 1.65e-19 -8.624
Metro_vs_SMC 0 5.388 3.37e-05 1.205
Metro_vs_SMC 1 6.483 3.27e-06 1.450
Metro_vs_SMC 2 5.180 5.33e-05 1.158
Metro_vs_SMC 3 7.204 7.66e-07 1.611
Metro_vs_SMC 4 10.189 3.89e-09 2.278
Metro_vs_DEMetro_Z 0 3.016 0.0071 0.674
Metro_vs_DEMetro_Z 1 -3.941 0.000877 -0.881
Metro_vs_DEMetro_Z 2 -11.573 4.77e-10 -2.588
Metro_vs_DEMetro_Z 3 -21.454 8.86e-15 -4.797
Metro_vs_DEMetro_Z 4 -38.132 2.04e-19 -8.526
HMC_vs_Metro 0 -4.585 0.000202 -1.025
HMC_vs_Metro 1 -5.972 9.53e-06 -1.335
HMC_vs_Metro 2 -4.701 0.000155 -1.051
HMC_vs_Metro 3 -5.864 1.2e-05 -1.311
HMC_vs_Metro 4 -7.440 4.84e-07 -1.664
HMC_vs_SMC 0 0.061 0.952 0.014
HMC_vs_SMC 1 2.312 0.0321 0.517
HMC_vs_SMC 2 3.270 0.00403 0.731
HMC_vs_SMC 3 3.384 0.00311 0.757
HMC_vs_SMC 4 6.526 2.99e-06 1.459
DEMetro_Z_vs_SMC 0 2.237 0.0375 0.500
DEMetro_Z_vs_SMC 1 4.055 0.000676 0.907
DEMetro_Z_vs_SMC 2 11.728 3.81e-10 2.622
DEMetro_Z_vs_SMC 3 22.933 2.61e-15 5.128
DEMetro_Z_vs_SMC 4 38.997 1.34e-19 8.720
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.024 0.022 0.013 0.144
HMC 5 0.035 0.019 0.011 1.513
HMC 10 0.040 0.016 0.010 2.389
HMC 15 0.054 0.020 0.011 3.066
HMC 30 0.096 0.022 0.013 5.668
SMC 2 0.024 0.022 0.013 0.117
SMC 5 0.019 0.019 0.011 0.003
SMC 10 0.019 0.016 0.010 0.241
SMC 15 0.021 0.020 0.011 0.031
SMC 30 0.016 0.022 0.013 -0.522
Metro 2 0.081 0.022 0.013 4.598
Metro 5 0.173 0.019 0.011 14.256
Metro 10 0.200 0.016 0.010 18.420
Metro 15 0.380 0.020 0.011 33.000
Metro 30 0.419 0.022 0.013 30.448
DEMetro_Z 2 0.040 0.022 0.013 1.381
DEMetro_Z 5 3.466 0.019 0.011 320.043
DEMetro_Z 10 8.054 0.016 0.010 807.819
DEMetro_Z 15 10.317 0.020 0.011 945.326
DEMetro_Z 30 11.953 0.022 0.013 915.814
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.185 0.00422 2.481
HMC 5 3.585 0.00178 3.933
HMC 10 4.556 0.000177 4.882
HMC 15 4.450 0.000186 3.277
HMC 30 3.977 0.000706 4.361
SMC 2 0.804 0.427 0.291
SMC 5 1.406 0.169 0.528
SMC 10 1.855 0.0738 0.880
SMC 15 1.770 0.0847 0.573
SMC 30 1.303 0.201 0.490
Metro 2 4.672 0.000133 4.860
Metro 5 5.278 4.1e-05 13.952
Metro 10 5.071 6.71e-05 27.228
Metro 15 6.213 5.41e-06 17.319
Metro 30 8.241 9.75e-08 22.585
DEMetro_Z 2 5.135 3.38e-05 3.741
DEMetro_Z 5 3.276 0.00397 2493.668
DEMetro_Z 10 7.651 3.23e-07 2479.958
DEMetro_Z 15 7.710 2.89e-07 1681.457
DEMetro_Z 30 9.113 2.3e-08 1654.760
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.192 0.00479 0.714
HMC_vs_SMC 1 3.300 0.00376 0.738
HMC_vs_SMC 2 3.587 0.00197 0.802
HMC_vs_SMC 3 4.240 0.000443 0.948
HMC_vs_SMC 4 3.421 0.00286 0.765
Metro_vs_DEMetro_Z 0 0.804 0.432 0.180
Metro_vs_DEMetro_Z 1 -3.259 0.00413 -0.729
Metro_vs_DEMetro_Z 2 -7.575 3.73e-07 -1.694
Metro_vs_DEMetro_Z 3 -7.662 3.16e-07 -1.713
Metro_vs_DEMetro_Z 4 -8.969 2.94e-08 -2.006
HMC_vs_Metro 0 -1.974 0.0631 -0.441
HMC_vs_Metro 1 -4.067 0.000658 -0.909
HMC_vs_Metro 2 -4.703 0.000155 -1.052
HMC_vs_Metro 3 -5.165 5.51e-05 -1.155
HMC_vs_Metro 4 -5.818 1.32e-05 -1.301
HMC_vs_DEMetro_Z 0 -1.126 0.274 -0.252
HMC_vs_DEMetro_Z 1 -3.270 0.00403 -0.731
HMC_vs_DEMetro_Z 2 -7.643 3.28e-07 -1.709
HMC_vs_DEMetro_Z 3 -7.692 2.99e-07 -1.720
HMC_vs_DEMetro_Z 4 -9.096 2.37e-08 -2.034
Metro_vs_SMC 0 4.115 0.000589 0.920
Metro_vs_SMC 1 5.220 4.88e-05 1.167
Metro_vs_SMC 2 4.834 0.000115 1.081
Metro_vs_SMC 3 5.944 1.01e-05 1.329
Metro_vs_SMC 4 7.822 2.34e-07 1.749
DEMetro_Z_vs_SMC 0 4.418 0.000295 0.988
DEMetro_Z_vs_SMC 1 3.275 0.00398 0.732
DEMetro_Z_vs_SMC 2 7.647 3.26e-07 1.710
DEMetro_Z_vs_SMC 3 7.709 2.89e-07 1.724
DEMetro_Z_vs_SMC 4 9.109 2.31e-08 2.037
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.045 0.019 0.010 2.481
HMC 5 0.057 0.022 0.009 3.933
HMC 10 0.068 0.024 0.009 4.882
HMC 15 0.072 0.024 0.015 3.277
HMC 30 0.082 0.025 0.013 4.361
SMC 2 0.023 0.019 0.010 0.291
SMC 5 0.027 0.022 0.009 0.528
SMC 10 0.032 0.024 0.009 0.880
SMC 15 0.033 0.024 0.015 0.573
SMC 30 0.032 0.025 0.013 0.490
Metro 2 0.070 0.019 0.010 4.860
Metro 5 0.147 0.022 0.009 13.952
Metro 10 0.266 0.024 0.009 27.228
Metro 15 0.279 0.024 0.015 17.319
Metro 30 0.321 0.025 0.013 22.585
DEMetro_Z 2 0.058 0.019 0.010 3.741
DEMetro_Z 5 22.394 0.022 0.009 2493.668
DEMetro_Z 10 22.007 0.024 0.009 2479.958
DEMetro_Z 15 24.811 0.024 0.015 1681.457
DEMetro_Z 30 21.693 0.025 0.013 1654.760
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.264 0.0305 0.958
HMC 5 3.937 0.000678 3.011
HMC 10 5.612 1.2e-05 4.566
HMC 15 5.325 3e-05 6.016
HMC 30 7.162 5.91e-07 9.367
SMC 2 -0.289 0.775 -0.112
SMC 5 0.453 0.653 0.154
SMC 10 1.512 0.139 0.564
SMC 15 0.417 0.679 0.151
SMC 30 -1.271 0.212 -0.354
Metro 2 5.921 7.75e-06 6.710
Metro 5 7.552 3.6e-07 21.438
Metro 10 6.998 1.13e-06 36.087
Metro 15 8.408 7.8e-08 53.470
Metro 30 10.691 1.68e-09 47.666
DEMetro_Z 2 4.930 4.67e-05 3.056
DEMetro_Z 5 4.246 0.000437 492.977
DEMetro_Z 10 12.675 1.02e-10 1334.695
DEMetro_Z 15 25.487 3.73e-16 1522.062
DEMetro_Z 30 38.822 1.45e-19 1416.972
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 2.728 0.0134 0.610
Metro_vs_DEMetro_Z 1 -4.123 0.000579 -0.922
Metro_vs_DEMetro_Z 2 -12.368 1.55e-10 -2.765
Metro_vs_DEMetro_Z 3 -23.702 1.42e-15 -5.300
Metro_vs_DEMetro_Z 4 -37.905 2.28e-19 -8.476
DEMetro_Z_vs_SMC 0 5.068 6.83e-05 1.133
DEMetro_Z_vs_SMC 1 4.243 0.00044 0.949
DEMetro_Z_vs_SMC 2 12.668 1.03e-10 2.833
DEMetro_Z_vs_SMC 3 25.504 3.68e-16 5.703
DEMetro_Z_vs_SMC 4 38.836 1.45e-19 8.684
HMC_vs_DEMetro_Z 0 -3.464 0.0026 -0.774
HMC_vs_DEMetro_Z 1 -4.218 0.000465 -0.943
HMC_vs_DEMetro_Z 2 -12.621 1.1e-10 -2.822
HMC_vs_DEMetro_Z 3 -25.527 3.62e-16 -5.708
HMC_vs_DEMetro_Z 4 -38.562 1.65e-19 -8.623
HMC_vs_Metro 0 -4.729 0.000146 -1.057
HMC_vs_Metro 1 -6.824 1.63e-06 -1.526
HMC_vs_Metro 2 -6.269 5.09e-06 -1.402
HMC_vs_Metro 3 -6.960 1.24e-06 -1.556
HMC_vs_Metro 4 -7.919 1.95e-07 -1.771
HMC_vs_SMC 0 2.066 0.0527 0.462
HMC_vs_SMC 1 4.123 0.000579 0.922
HMC_vs_SMC 2 4.991 8.1e-05 1.116
HMC_vs_SMC 3 5.428 3.09e-05 1.214
HMC_vs_SMC 4 7.534 4.04e-07 1.685
Metro_vs_SMC 0 6.564 2.77e-06 1.468
Metro_vs_SMC 1 7.805 2.41e-07 1.745
Metro_vs_SMC 2 7.039 1.06e-06 1.574
Metro_vs_SMC 3 8.420 7.77e-08 1.883
Metro_vs_SMC 4 10.844 1.41e-09 2.425
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.037 0.029 0.008 0.958
HMC 5 0.044 0.025 0.006 3.011
HMC 10 0.046 0.022 0.005 4.566
HMC 15 0.059 0.024 0.006 6.016
HMC 30 0.091 0.026 0.007 9.367
SMC 2 0.028 0.029 0.008 -0.112
SMC 5 0.025 0.025 0.006 0.154
SMC 10 0.025 0.022 0.005 0.564
SMC 15 0.025 0.024 0.006 0.151
SMC 30 0.023 0.026 0.007 -0.354
Metro 2 0.084 0.029 0.008 6.710
Metro 5 0.160 0.025 0.006 21.438
Metro 10 0.213 0.022 0.005 36.087
Metro 15 0.335 0.024 0.006 53.470
Metro 30 0.356 0.026 0.007 47.666
DEMetro_Z 2 0.054 0.029 0.008 3.056
DEMetro_Z 5 3.150 0.025 0.006 492.977
DEMetro_Z 10 7.062 0.022 0.005 1334.695
DEMetro_Z 15 8.877 0.024 0.006 1522.062
DEMetro_Z 30 9.849 0.026 0.007 1416.972
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.598 0.0135 0.933
HMC 5 4.102 0.000401 2.612
HMC 10 5.192 3.59e-05 4.733
HMC 15 5.768 9.25e-06 5.229
HMC 30 7.589 2.36e-07 9.307
SMC 2 -1.037 0.307 -0.366
SMC 5 0.550 0.586 0.163
SMC 10 1.353 0.186 0.559
SMC 15 0.698 0.49 0.246
SMC 30 -0.361 0.72 -0.118
Metro 2 5.203 4.04e-05 6.106
Metro 5 8.120 1.14e-07 16.912
Metro 10 9.339 1.47e-08 35.725
Metro 15 8.481 6.76e-08 43.297
Metro 30 12.584 1.05e-10 46.150
DEMetro_Z 2 4.708 7.19e-05 2.612
DEMetro_Z 5 10.577 2.1e-09 108.957
DEMetro_Z 10 47.279 3.16e-21 257.915
DEMetro_Z 15 80.704 7.07e-26 205.642
DEMetro_Z 30 57.686 6.11e-23 206.492
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.341 3.73e-05 1.194
DEMetro_Z_vs_SMC 1 10.578 2.11e-09 2.365
DEMetro_Z_vs_SMC 2 47.819 2.88e-21 10.693
DEMetro_Z_vs_SMC 3 84.984 5.46e-26 19.003
DEMetro_Z_vs_SMC 4 58.754 5.91e-23 13.138
HMC_vs_Metro 0 -4.275 0.000409 -0.956
HMC_vs_Metro 1 -7.254 6.94e-07 -1.622
HMC_vs_Metro 2 -8.037 1.56e-07 -1.797
HMC_vs_Metro 3 -7.103 9.35e-07 -1.588
HMC_vs_Metro 4 -8.836 3.71e-08 -1.976
Metro_vs_DEMetro_Z 0 2.460 0.0236 0.550
Metro_vs_DEMetro_Z 1 -9.725 8.24e-09 -2.175
Metro_vs_DEMetro_Z 2 -34.839 1.11e-18 -7.790
Metro_vs_DEMetro_Z 3 -25.733 3.12e-16 -5.754
Metro_vs_DEMetro_Z 4 -35.007 1.01e-18 -7.828
HMC_vs_SMC 0 3.227 0.00444 0.722
HMC_vs_SMC 1 4.321 0.000368 0.966
HMC_vs_SMC 2 4.494 0.000248 1.005
HMC_vs_SMC 3 6.313 4.65e-06 1.412
HMC_vs_SMC 4 7.617 3.45e-07 1.703
Metro_vs_SMC 0 5.897 1.12e-05 1.319
Metro_vs_SMC 1 8.053 1.52e-07 1.801
Metro_vs_SMC 2 9.397 1.42e-08 2.101
Metro_vs_SMC 3 8.354 8.76e-08 1.868
Metro_vs_SMC 4 12.678 1.02e-10 2.835
HMC_vs_DEMetro_Z 0 -3.330 0.00352 -0.745
HMC_vs_DEMetro_Z 1 -10.338 3.07e-09 -2.312
HMC_vs_DEMetro_Z 2 -42.276 2.94e-20 -9.453
HMC_vs_DEMetro_Z 3 -79.147 2.1e-25 -17.698
HMC_vs_DEMetro_Z 4 -49.474 1.52e-21 -11.063
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.020 0.015 0.005 0.933
HMC 5 0.026 0.013 0.005 2.612
HMC 10 0.028 0.012 0.003 4.733
HMC 15 0.037 0.014 0.004 5.229
HMC 30 0.058 0.015 0.005 9.307
SMC 2 0.014 0.015 0.005 -0.366
SMC 5 0.014 0.013 0.005 0.163
SMC 10 0.014 0.012 0.003 0.559
SMC 15 0.015 0.014 0.004 0.246
SMC 30 0.014 0.015 0.005 -0.118
Metro 2 0.045 0.015 0.005 6.106
Metro 5 0.095 0.013 0.005 16.912
Metro 10 0.133 0.012 0.003 35.725
Metro 15 0.204 0.014 0.004 43.297
Metro 30 0.227 0.015 0.005 46.150
DEMetro_Z 2 0.028 0.015 0.005 2.612
DEMetro_Z 5 0.540 0.013 0.005 108.957
DEMetro_Z 10 0.886 0.012 0.003 257.915
DEMetro_Z 15 0.917 0.014 0.004 205.642
DEMetro_Z 30 0.963 0.015 0.005 206.492
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_heavy_Tails (MvStudentT, dimension, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.634 0.111 0.562
HMC 5 -2.370 0.0244 -0.609
HMC 10 -0.683 0.499 -0.200
HMC 15 1.805 0.0852 1.682
HMC 30 2.303 0.0327 15.082
SMC 2 3.253 0.0024 1.043
SMC 5 14.090 1.25e-11 32.987
SMC 10 10.375 1.48e-10 6.188
SMC 15 25.505 2.93e-16 84.604
SMC 30 72.503 1.01e-24 499.715
Metro 2 2.030 0.0498 0.745
Metro 5 4.400 0.000225 3.582
Metro 10 1.355 0.184 0.431
Metro 15 2.962 0.00796 11.124
Metro 30 3.804 0.0012 89.465
DEMetro_Z 2 3.511 0.00139 1.534
DEMetro_Z 5 7.131 8.84e-07 233.960
DEMetro_Z 10 5.264 4.37e-05 26.129
DEMetro_Z 15 19.522 4.9e-14 307.924
DEMetro_Z 30 23.829 1.29e-15 1805.514
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.115 0.0478 -0.473
HMC_vs_DEMetro_Z 1 -7.148 8.56e-07 -1.598
HMC_vs_DEMetro_Z 2 -5.416 3.16e-05 -1.211
HMC_vs_DEMetro_Z 3 -19.171 6.87e-14 -4.287
HMC_vs_DEMetro_Z 4 -23.933 1.19e-15 -5.352
Metro_vs_SMC 0 -0.802 0.432 -0.179
Metro_vs_SMC 1 -12.997 6.65e-11 -2.906
Metro_vs_SMC 2 -12.520 1.26e-10 -2.799
Metro_vs_SMC 3 -14.480 1.02e-11 -3.238
Metro_vs_SMC 4 -16.758 7.72e-13 -3.747
Metro_vs_DEMetro_Z 0 -1.414 0.174 -0.316
Metro_vs_DEMetro_Z 1 -7.009 1.13e-06 -1.567
Metro_vs_DEMetro_Z 2 -5.300 4.08e-05 -1.185
Metro_vs_DEMetro_Z 3 -18.792 9.86e-14 -4.202
Metro_vs_DEMetro_Z 4 -20.188 2.69e-14 -4.514
HMC_vs_Metro 0 -0.485 0.633 -0.108
HMC_vs_Metro 1 -5.713 1.66e-05 -1.278
HMC_vs_Metro 2 -2.175 0.0425 -0.486
HMC_vs_Metro 3 -2.363 0.0289 -0.528
HMC_vs_Metro 4 -3.001 0.00735 -0.671
HMC_vs_SMC 0 -1.169 0.257 -0.261
HMC_vs_SMC 1 -14.665 8.18e-12 -3.279
HMC_vs_SMC 2 -11.003 1.11e-09 -2.460
HMC_vs_SMC 3 -27.904 6.96e-17 -6.239
HMC_vs_SMC 4 -46.168 5.59e-21 -10.324
DEMetro_Z_vs_SMC 0 1.032 0.315 0.231
DEMetro_Z_vs_SMC 1 6.187 6.05e-06 1.383
DEMetro_Z_vs_SMC 2 4.157 0.000535 0.930
DEMetro_Z_vs_SMC 3 13.834 2.26e-11 3.093
DEMetro_Z_vs_SMC 4 17.362 4.1e-13 3.882
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.088 0.066 0.039 0.562
HMC 5 0.050 0.067 0.029 -0.609
HMC 10 0.077 0.095 0.090 -0.200
HMC 15 0.085 0.063 0.013 1.682
HMC 30 0.202 0.064 0.009 15.082
SMC 2 0.107 0.066 0.039 1.043
SMC 5 1.014 0.067 0.029 32.987
SMC 10 0.650 0.095 0.090 6.188
SMC 15 1.176 0.063 0.013 84.604
SMC 30 4.621 0.064 0.009 499.715
Metro 2 0.096 0.066 0.039 0.745
Metro 5 0.170 0.067 0.029 3.582
Metro 10 0.134 0.095 0.090 0.431
Metro 15 0.209 0.063 0.013 11.124
Metro 30 0.880 0.064 0.009 89.465
DEMetro_Z 2 0.127 0.066 0.039 1.534
DEMetro_Z 5 6.781 0.067 0.029 233.960
DEMetro_Z 10 2.438 0.095 0.090 26.129
DEMetro_Z 15 4.116 0.063 0.013 307.924
DEMetro_Z 30 16.528 0.064 0.009 1805.514
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.531 0.599 -0.142
HMC 5 -0.264 0.794 -0.065
HMC 10 -1.224 0.236 -0.274
HMC 15 0.726 0.472 0.237
HMC 30 1.390 0.18 2.208
SMC 2 0.671 0.508 0.162
SMC 5 22.793 1.8e-15 49.971
SMC 10 13.489 7.48e-12 3.100
SMC 15 61.035 2.09e-23 220.291
SMC 30 158.288 3.44e-31 922.805
Metro 2 -0.571 0.572 -0.149
Metro 5 -0.583 0.566 -0.135
Metro 10 -1.192 0.248 -0.267
Metro 15 1.093 0.288 4.322
Metro 30 1.673 0.111 52.068
DEMetro_Z 2 -0.558 0.581 -0.149
DEMetro_Z 5 5.148 5.71e-05 88.770
DEMetro_Z 10 1.756 0.0872 0.540
DEMetro_Z 15 10.013 4.92e-09 46.319
DEMetro_Z 30 19.679 4.26e-14 488.501
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -2.112 0.0482 -0.472
HMC_vs_SMC 1 -22.581 3.47e-15 -5.049
HMC_vs_SMC 2 -65.626 7.3e-24 -14.674
HMC_vs_SMC 3 -59.898 4.11e-23 -13.394
HMC_vs_SMC 4 -142.661 2.95e-30 -31.900
Metro_vs_DEMetro_Z 0 -0.020 0.984 -0.004
Metro_vs_DEMetro_Z 1 -5.153 5.65e-05 -1.152
Metro_vs_DEMetro_Z 2 -3.862 0.00105 -0.864
Metro_vs_DEMetro_Z 3 -8.148 1.27e-07 -1.822
Metro_vs_DEMetro_Z 4 -9.708 8.46e-09 -2.171
HMC_vs_Metro 0 0.104 0.918 0.023
HMC_vs_Metro 1 0.542 0.594 0.121
HMC_vs_Metro 2 -2.648 0.0159 -0.592
HMC_vs_Metro 3 -1.030 0.316 -0.230
HMC_vs_Metro 4 -1.601 0.126 -0.358
HMC_vs_DEMetro_Z 0 0.095 0.926 0.021
HMC_vs_DEMetro_Z 1 -5.167 5.49e-05 -1.155
HMC_vs_DEMetro_Z 2 -3.862 0.00105 -0.864
HMC_vs_DEMetro_Z 3 -9.939 5.81e-09 -2.222
HMC_vs_DEMetro_Z 4 -19.411 5.48e-14 -4.340
Metro_vs_SMC 0 -2.495 0.022 -0.558
Metro_vs_SMC 1 -22.991 2.49e-15 -5.141
Metro_vs_SMC 2 -65.913 6.72e-24 -14.739
Metro_vs_SMC 3 -46.264 5.38e-21 -10.345
Metro_vs_SMC 4 -27.014 1.27e-16 -6.041
DEMetro_Z_vs_SMC 0 -2.281 0.0343 -0.510
DEMetro_Z_vs_SMC 1 2.110 0.0483 0.472
DEMetro_Z_vs_SMC 2 -12.032 2.48e-10 -2.690
DEMetro_Z_vs_SMC 3 -32.647 3.74e-18 -7.300
DEMetro_Z_vs_SMC 4 -16.191 1.42e-12 -3.621
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 7.146 9.309 15.244 -0.142
HMC 5 8.322 9.700 21.181 -0.065
HMC 10 4.641 73.432 251.325 -0.274
HMC 15 9.576 7.127 10.327 0.237
HMC 30 25.392 6.949 8.351 2.208
SMC 2 11.774 9.309 15.244 0.162
SMC 5 1068.147 9.700 21.181 49.971
SMC 10 852.478 73.432 251.325 3.100
SMC 15 2282.080 7.127 10.327 220.291
SMC 30 7713.644 6.949 8.351 922.805
Metro 2 7.031 9.309 15.244 -0.149
Metro 5 6.849 9.700 21.181 -0.135
Metro 10 6.403 73.432 251.325 -0.267
Metro 15 51.763 7.127 10.327 4.322
Metro 30 441.787 6.949 8.351 52.068
DEMetro_Z 2 7.040 9.309 15.244 -0.149
DEMetro_Z 5 1889.968 9.700 21.181 88.770
DEMetro_Z 10 209.078 73.432 251.325 0.540
DEMetro_Z 15 485.461 7.127 10.327 46.319
DEMetro_Z 30 4086.605 6.949 8.351 488.501
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.310 0.0023 1.380
HMC 5 2.278 0.0331 2.070
HMC 10 1.556 0.129 0.635
HMC 15 5.296 3.7e-05 9.179
HMC 30 2.670 0.0151 47.942
SMC 2 10.172 2.73e-09 16.566
SMC 5 35.695 6.99e-19 788.805
SMC 10 102.575 6.95e-28 260.283
SMC 15 112.632 2.55e-28 1666.872
SMC 30 320.242 6.19e-37 6134.686
Metro 2 4.553 9.66e-05 2.311
Metro 5 5.070 6.17e-05 8.774
Metro 10 3.841 0.000717 2.185
Metro 15 2.002 0.0598 33.656
Metro 30 4.191 0.000495 510.175
DEMetro_Z 2 8.073 7.15e-09 3.885
DEMetro_Z 5 10.405 2.77e-09 604.387
DEMetro_Z 10 8.024 1.59e-07 83.393
DEMetro_Z 15 20.219 2.61e-14 665.509
DEMetro_Z 30 40.352 7.05e-20 4274.775
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.281 0.0342 -0.510
Metro_vs_DEMetro_Z 1 -10.189 3.89e-09 -2.278
Metro_vs_DEMetro_Z 2 -8.094 1.41e-07 -1.810
Metro_vs_DEMetro_Z 3 -19.645 4.41e-14 -4.393
Metro_vs_DEMetro_Z 4 -20.198 2.66e-14 -4.517
DEMetro_Z_vs_SMC 0 -7.195 7.8e-07 -1.609
DEMetro_Z_vs_SMC 1 -2.669 0.0152 -0.597
DEMetro_Z_vs_SMC 2 -16.553 9.61e-13 -3.701
DEMetro_Z_vs_SMC 3 -30.923 1.03e-17 -6.915
DEMetro_Z_vs_SMC 4 -16.491 1.03e-12 -3.687
HMC_vs_DEMetro_Z 0 -4.357 0.000339 -0.974
HMC_vs_DEMetro_Z 1 -10.376 2.9e-09 -2.320
HMC_vs_DEMetro_Z 2 -8.067 1.48e-07 -1.804
HMC_vs_DEMetro_Z 3 -20.106 2.89e-14 -4.496
HMC_vs_DEMetro_Z 4 -38.995 1.34e-19 -8.720
HMC_vs_Metro 0 -1.624 0.121 -0.363
HMC_vs_Metro 1 -3.523 0.00228 -0.788
HMC_vs_Metro 2 -3.654 0.00169 -0.817
HMC_vs_Metro 3 -1.544 0.139 -0.345
HMC_vs_Metro 4 -3.779 0.00127 -0.845
HMC_vs_SMC 0 -9.217 1.92e-08 -2.061
HMC_vs_SMC 1 -35.410 8.18e-19 -7.918
HMC_vs_SMC 2 -104.392 1.11e-27 -23.343
HMC_vs_SMC 3 -119.098 9.07e-29 -26.631
HMC_vs_SMC 4 -244.544 1.06e-34 -54.682
Metro_vs_SMC 0 -8.387 8.25e-08 -1.875
Metro_vs_SMC 1 -35.715 6.96e-19 -7.986
Metro_vs_SMC 2 -98.816 3.13e-27 -22.096
Metro_vs_SMC 3 -83.836 7.07e-26 -18.746
Metro_vs_SMC 4 -45.352 7.83e-21 -10.141
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.176 0.124 0.038 1.380
HMC 5 0.174 0.117 0.027 2.070
HMC 10 0.201 0.149 0.082 0.635
HMC 15 0.319 0.119 0.022 9.179
HMC 30 0.646 0.116 0.011 47.942
SMC 2 0.748 0.124 0.038 16.566
SMC 5 21.528 0.117 0.027 788.805
SMC 10 21.459 0.149 0.082 260.283
SMC 15 36.376 0.119 0.022 1666.872
SMC 30 67.819 0.116 0.011 6134.686
Metro 2 0.211 0.124 0.038 2.311
Metro 5 0.356 0.117 0.027 8.774
Metro 10 0.327 0.149 0.082 2.185
Metro 15 0.851 0.119 0.022 33.656
Metro 30 5.747 0.116 0.011 510.175
DEMetro_Z 2 0.271 0.124 0.038 3.885
DEMetro_Z 5 16.522 0.117 0.027 604.387
DEMetro_Z 10 6.976 0.149 0.082 83.393
DEMetro_Z 15 14.595 0.119 0.022 665.509
DEMetro_Z 30 47.293 0.116 0.011 4274.775
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.245 0.0349 1.685
HMC 5 5.207 1.87e-05 2.840
HMC 10 2.795 0.0115 13.563
HMC 15 4.538 0.000223 25.231
HMC 30 5.112 6.17e-05 42.944
SMC 2 14.564 5.9e-12 27.125
SMC 5 130.989 3.49e-30 257.773
SMC 10 142.223 4.85e-31 250.816
SMC 15 150.888 8.78e-32 234.845
SMC 30 163.890 3.5e-33 200.749
Metro 2 5.799 5.46e-06 3.719
Metro 5 9.057 2.21e-08 22.964
Metro 10 6.936 1.25e-06 24.401
Metro 15 7.200 7.59e-07 42.629
Metro 30 19.324 5.8e-14 172.664
DEMetro_Z 2 7.351 2.81e-07 6.804
DEMetro_Z 5 38.211 1.82e-19 248.132
DEMetro_Z 10 44.471 1.01e-20 251.536
DEMetro_Z 15 56.678 9.77e-23 268.316
DEMetro_Z 30 76.679 2.36e-25 235.293
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -10.254 3.51e-09 -2.293
DEMetro_Z_vs_SMC 1 -1.526 0.144 -0.341
DEMetro_Z_vs_SMC 2 0.118 0.907 0.026
DEMetro_Z_vs_SMC 3 6.720 2.01e-06 1.503
DEMetro_Z_vs_SMC 4 10.682 1.8e-09 2.389
HMC_vs_Metro 0 -2.015 0.0583 -0.451
HMC_vs_Metro 1 -7.748 2.69e-07 -1.732
HMC_vs_Metro 2 -2.812 0.0111 -0.629
HMC_vs_Metro 3 -2.308 0.0324 -0.516
HMC_vs_Metro 4 -11.483 5.43e-10 -2.568
Metro_vs_DEMetro_Z 0 -2.523 0.0207 -0.564
Metro_vs_DEMetro_Z 1 -32.486 4.1e-18 -7.264
Metro_vs_DEMetro_Z 2 -41.262 4.63e-20 -9.226
Metro_vs_DEMetro_Z 3 -27.074 1.22e-16 -6.054
Metro_vs_DEMetro_Z 4 -6.526 2.99e-06 -1.459
HMC_vs_SMC 0 -12.149 2.1e-10 -2.717
HMC_vs_SMC 1 -129.002 1.99e-29 -28.846
HMC_vs_SMC 2 -45.091 8.73e-21 -10.083
HMC_vs_SMC 3 -39.232 1.2e-19 -8.773
HMC_vs_SMC 4 -17.499 3.56e-13 -3.913
Metro_vs_SMC 0 -11.465 5.57e-10 -2.564
Metro_vs_SMC 1 -83.382 7.83e-26 -18.645
Metro_vs_SMC 2 -53.465 3.51e-22 -11.955
Metro_vs_SMC 3 -29.104 3.18e-17 -6.508
Metro_vs_SMC 4 -3.104 0.00584 -0.694
HMC_vs_DEMetro_Z 0 -4.807 0.000122 -1.075
HMC_vs_DEMetro_Z 1 -37.273 3.13e-19 -8.334
HMC_vs_DEMetro_Z 2 -37.072 3.46e-19 -8.290
HMC_vs_DEMetro_Z 3 -27.973 6.65e-17 -6.255
HMC_vs_DEMetro_Z 4 -20.999 1.31e-14 -4.696
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.022 0.014 0.005 1.685
HMC 5 0.020 0.015 0.002 2.840
HMC 10 0.039 0.015 0.002 13.563
HMC 15 0.061 0.016 0.002 25.231
HMC 30 0.101 0.015 0.002 42.944
SMC 2 0.141 0.014 0.005 27.125
SMC 5 0.505 0.015 0.002 257.773
SMC 10 0.456 0.015 0.002 250.816
SMC 15 0.436 0.016 0.002 234.845
SMC 30 0.414 0.015 0.002 200.749
Metro 2 0.032 0.014 0.005 3.719
Metro 5 0.058 0.015 0.002 22.964
Metro 10 0.058 0.015 0.002 24.401
Metro 15 0.092 0.016 0.002 42.629
Metro 30 0.359 0.015 0.002 172.664
DEMetro_Z 2 0.046 0.014 0.005 6.804
DEMetro_Z 5 0.487 0.015 0.002 248.132
DEMetro_Z 10 0.457 0.015 0.002 251.536
DEMetro_Z 15 0.495 0.016 0.002 268.316
DEMetro_Z 30 0.483 0.015 0.002 235.293
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.092 0.282 -0.332
HMC 5 0.876 0.387 0.300
HMC 10 -1.327 0.199 -0.302
HMC 15 1.413 0.174 4.591
HMC 30 1.180 0.253 8.451
SMC 2 1.450 0.156 0.558
SMC 5 4.819 0.000119 41.142
SMC 10 7.481 2.42e-07 7.596
SMC 15 18.443 1.25e-13 82.493
SMC 30 39.928 8.35e-20 426.800
Metro 2 3.120 0.00399 1.428
Metro 5 2.697 0.0123 1.595
Metro 10 0.810 0.424 0.209
Metro 15 3.524 0.00219 6.697
Metro 30 5.040 7.23e-05 38.312
DEMetro_Z 2 2.536 0.0161 1.029
DEMetro_Z 5 4.064 0.000661 68.636
DEMetro_Z 10 6.632 2.2e-06 15.530
DEMetro_Z 15 9.857 6.63e-09 304.163
DEMetro_Z 30 12.023 2.51e-10 1409.414
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.903 0.00912 -0.649
HMC_vs_DEMetro_Z 1 -4.026 0.000722 -0.900
HMC_vs_DEMetro_Z 2 -6.809 1.68e-06 -1.522
HMC_vs_DEMetro_Z 3 -9.490 1.21e-08 -2.122
HMC_vs_DEMetro_Z 4 -11.847 3.22e-10 -2.649
Metro_vs_SMC 0 1.711 0.103 0.383
Metro_vs_SMC 1 -4.618 0.000188 -1.033
Metro_vs_SMC 2 -7.194 7.82e-07 -1.609
Metro_vs_SMC 3 -14.800 6.97e-12 -3.309
Metro_vs_SMC 4 -31.586 6.93e-18 -7.063
Metro_vs_DEMetro_Z 0 0.788 0.44 0.176
Metro_vs_DEMetro_Z 1 -3.959 0.000841 -0.885
Metro_vs_DEMetro_Z 2 -6.652 2.31e-06 -1.487
Metro_vs_DEMetro_Z 3 -9.497 1.2e-08 -2.124
Metro_vs_DEMetro_Z 4 -11.951 2.78e-10 -2.672
HMC_vs_Metro 0 -3.846 0.00109 -0.860
HMC_vs_Metro 1 -1.967 0.064 -0.440
HMC_vs_Metro 2 -3.816 0.00117 -0.853
HMC_vs_Metro 3 -0.544 0.593 -0.122
HMC_vs_Metro 4 -2.899 0.00921 -0.648
HMC_vs_SMC 0 -2.563 0.019 -0.573
HMC_vs_SMC 1 -4.758 0.000137 -1.064
HMC_vs_SMC 2 -7.920 1.95e-07 -1.771
HMC_vs_SMC 3 -13.784 2.41e-11 -3.082
HMC_vs_SMC 4 -33.897 1.85e-18 -7.580
DEMetro_Z_vs_SMC 0 1.119 0.277 0.250
DEMetro_Z_vs_SMC 1 1.850 0.0799 0.414
DEMetro_Z_vs_SMC 2 3.007 0.00725 0.672
DEMetro_Z_vs_SMC 3 7.208 7.61e-07 1.612
DEMetro_Z_vs_SMC 4 8.442 7.47e-08 1.888
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.053 0.066 0.039 -0.332
HMC 5 0.076 0.067 0.029 0.300
HMC 10 0.068 0.095 0.090 -0.302
HMC 15 0.123 0.063 0.013 4.591
HMC 30 0.141 0.064 0.009 8.451
SMC 2 0.088 0.066 0.039 0.558
SMC 5 1.248 0.067 0.029 41.142
SMC 10 0.777 0.095 0.090 7.596
SMC 15 1.149 0.063 0.013 82.493
SMC 30 3.956 0.064 0.009 426.800
Metro 2 0.122 0.066 0.039 1.428
Metro 5 0.113 0.067 0.029 1.595
Metro 10 0.114 0.095 0.090 0.209
Metro 15 0.151 0.063 0.013 6.697
Metro 30 0.413 0.064 0.009 38.312
DEMetro_Z 2 0.107 0.066 0.039 1.029
DEMetro_Z 5 2.037 0.067 0.029 68.636
DEMetro_Z 10 1.488 0.095 0.090 15.530
DEMetro_Z 15 4.066 0.063 0.013 304.163
DEMetro_Z 30 12.916 0.064 0.009 1409.414
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.827 0.415 -0.217
HMC 5 -0.268 0.791 -0.065
HMC 10 -1.222 0.237 -0.273
HMC 15 1.012 0.324 1.389
HMC 30 1.036 0.312 1.042
SMC 2 -0.279 0.782 -0.071
SMC 5 11.645 3.87e-10 39.553
SMC 10 10.517 3.84e-11 2.615
SMC 15 61.511 1.68e-23 200.029
SMC 30 82.718 8.73e-26 867.705
Metro 2 -0.733 0.469 -0.197
Metro 5 -0.841 0.41 -0.190
Metro 10 -1.217 0.239 -0.272
Metro 15 1.196 0.243 0.709
Metro 30 2.461 0.0235 6.921
DEMetro_Z 2 -0.521 0.606 -0.138
DEMetro_Z 5 1.846 0.0805 19.264
DEMetro_Z 10 -0.296 0.77 -0.069
DEMetro_Z 15 5.026 7.44e-05 29.033
DEMetro_Z 30 6.807 1.69e-06 197.299
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -1.358 0.19 -0.304
HMC_vs_SMC 1 -11.665 4.17e-10 -2.608
HMC_vs_SMC 2 -26.295 2.09e-16 -5.880
HMC_vs_SMC 3 -60.495 3.4e-23 -13.527
HMC_vs_SMC 4 -81.622 1.17e-25 -18.251
Metro_vs_DEMetro_Z 0 -2.511 0.0213 -0.561
Metro_vs_DEMetro_Z 1 -1.867 0.0774 -0.418
Metro_vs_DEMetro_Z 2 -2.917 0.00884 -0.652
Metro_vs_DEMetro_Z 3 -4.837 0.000115 -1.082
Metro_vs_DEMetro_Z 4 -6.788 1.76e-06 -1.518
HMC_vs_Metro 0 -0.801 0.433 -0.179
HMC_vs_Metro 1 1.260 0.223 0.282
HMC_vs_Metro 2 -0.439 0.665 -0.098
HMC_vs_Metro 3 0.451 0.657 0.101
HMC_vs_Metro 4 -2.098 0.0495 -0.469
HMC_vs_DEMetro_Z 0 -4.523 0.000233 -1.011
HMC_vs_DEMetro_Z 1 -1.852 0.0796 -0.414
HMC_vs_DEMetro_Z 2 -2.879 0.00962 -0.644
HMC_vs_DEMetro_Z 3 -4.937 9.16e-05 -1.104
HMC_vs_DEMetro_Z 4 -6.770 1.82e-06 -1.514
Metro_vs_SMC 0 -1.167 0.258 -0.261
Metro_vs_SMC 1 -11.777 3.56e-10 -2.633
Metro_vs_SMC 2 -26.394 1.95e-16 -5.902
Metro_vs_SMC 3 -60.980 2.93e-23 -13.636
Metro_vs_SMC 4 -80.356 1.58e-25 -17.968
DEMetro_Z_vs_SMC 0 -0.647 0.525 -0.145
DEMetro_Z_vs_SMC 1 -1.918 0.0703 -0.429
DEMetro_Z_vs_SMC 2 -22.659 3.26e-15 -5.067
DEMetro_Z_vs_SMC 3 -27.471 9.3e-17 -6.143
DEMetro_Z_vs_SMC 4 -22.799 2.91e-15 -5.098
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 5.996 9.309 15.244 -0.217
HMC 5 8.328 9.700 21.181 -0.065
HMC 10 4.751 73.432 251.325 -0.273
HMC 15 21.468 7.127 10.327 1.389
HMC 30 15.655 6.949 8.351 1.042
SMC 2 8.223 9.309 15.244 -0.071
SMC 5 847.485 9.700 21.181 39.553
SMC 10 730.602 73.432 251.325 2.615
SMC 15 2072.829 7.127 10.327 200.029
SMC 30 7253.480 6.949 8.351 867.705
Metro 2 6.311 9.309 15.244 -0.197
Metro 5 5.667 9.700 21.181 -0.190
Metro 10 5.051 73.432 251.325 -0.272
Metro 15 14.448 7.127 10.327 0.709
Metro 30 64.747 6.949 8.351 6.921
DEMetro_Z 2 7.206 9.309 15.244 -0.138
DEMetro_Z 5 417.735 9.700 21.181 19.264
DEMetro_Z 10 56.011 73.432 251.325 -0.069
DEMetro_Z 15 306.951 7.127 10.327 29.033
DEMetro_Z 30 1654.669 6.949 8.351 197.299
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.794 0.433 0.222
HMC 5 3.921 0.000571 2.177
HMC 10 1.728 0.0926 0.487
HMC 15 1.195 0.247 26.379
HMC 30 2.513 0.0211 37.148
SMC 2 5.273 3.92e-05 9.368
SMC 5 20.586 1.88e-14 692.291
SMC 10 45.527 6.38e-21 237.719
SMC 15 111.999 2.83e-28 1582.750
SMC 30 159.974 3.34e-31 5947.322
Metro 2 5.519 5.63e-06 2.557
Metro 5 7.695 5.56e-08 4.826
Metro 10 3.919 0.000382 1.416
Metro 15 3.576 0.002 16.051
Metro 30 3.951 0.000856 169.227
DEMetro_Z 2 6.721 1.55e-07 2.906
DEMetro_Z 5 4.704 0.000155 162.816
DEMetro_Z 10 6.564 2.73e-06 39.654
DEMetro_Z 15 9.531 1.13e-08 511.201
DEMetro_Z 30 14.114 1.6e-11 2555.528
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.659 0.518 -0.147
Metro_vs_DEMetro_Z 1 -4.561 0.000214 -1.020
Metro_vs_DEMetro_Z 2 -6.344 4.36e-06 -1.419
Metro_vs_DEMetro_Z 3 -9.127 2.25e-08 -2.041
Metro_vs_DEMetro_Z 4 -14.051 1.73e-11 -3.142
DEMetro_Z_vs_SMC 0 -3.716 0.00147 -0.831
DEMetro_Z_vs_SMC 1 -10.639 1.92e-09 -2.379
DEMetro_Z_vs_SMC 2 -26.274 2.13e-16 -5.875
DEMetro_Z_vs_SMC 3 -19.780 3.89e-14 -4.423
DEMetro_Z_vs_SMC 4 -19.060 7.63e-14 -4.262
HMC_vs_DEMetro_Z 0 -8.130 1.32e-07 -1.818
HMC_vs_DEMetro_Z 1 -4.615 0.000189 -1.032
HMC_vs_DEMetro_Z 2 -6.532 2.95e-06 -1.461
HMC_vs_DEMetro_Z 3 -9.148 2.17e-08 -2.045
HMC_vs_DEMetro_Z 4 -13.674 2.77e-11 -3.057
HMC_vs_Metro 0 -6.078 7.62e-06 -1.359
HMC_vs_Metro 1 -3.703 0.00151 -0.828
HMC_vs_Metro 2 -2.675 0.015 -0.598
HMC_vs_Metro 3 0.447 0.66 0.100
HMC_vs_Metro 4 -2.758 0.0125 -0.617
HMC_vs_SMC 0 -5.255 4.51e-05 -1.175
HMC_vs_SMC 1 -20.530 1.98e-14 -4.591
HMC_vs_SMC 2 -45.475 7.44e-21 -10.169
HMC_vs_SMC 3 -63.895 1.21e-23 -14.287
HMC_vs_SMC 4 -131.058 1.48e-29 -29.306
Metro_vs_SMC 0 -3.742 0.00138 -0.837
Metro_vs_SMC 1 -20.620 1.83e-14 -4.611
Metro_vs_SMC 2 -44.944 9.28e-21 -10.050
Metro_vs_SMC 3 -108.838 5.01e-28 -24.337
Metro_vs_SMC 4 -111.895 2.96e-28 -25.021
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.133 0.124 0.038 0.222
HMC 5 0.177 0.117 0.027 2.177
HMC 10 0.188 0.149 0.082 0.487
HMC 15 0.693 0.119 0.022 26.379
HMC 30 0.526 0.116 0.011 37.148
SMC 2 0.477 0.124 0.038 9.368
SMC 5 18.908 0.117 0.027 692.291
SMC 10 19.612 0.149 0.082 237.719
SMC 15 34.546 0.119 0.022 1582.750
SMC 30 65.751 0.116 0.011 5947.322
Metro 2 0.221 0.124 0.038 2.557
Metro 5 0.248 0.117 0.027 4.826
Metro 10 0.264 0.149 0.082 1.416
Metro 15 0.468 0.119 0.022 16.051
Metro 30 1.984 0.116 0.011 169.227
DEMetro_Z 2 0.234 0.124 0.038 2.906
DEMetro_Z 5 4.537 0.117 0.027 162.816
DEMetro_Z 10 3.395 0.149 0.082 39.654
DEMetro_Z 15 11.239 0.119 0.022 511.201
DEMetro_Z 30 28.319 0.116 0.011 2555.528
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.637 0.11 0.461
HMC 5 5.239 2.32e-05 3.463
HMC 10 5.924 8.62e-06 8.395
HMC 15 1.854 0.0794 24.950
HMC 30 2.278 0.0344 41.016
SMC 2 7.227 6.62e-07 17.524
SMC 5 61.581 1.94e-23 264.590
SMC 10 123.994 1.13e-29 253.604
SMC 15 125.749 6.82e-30 237.483
SMC 30 157.186 1.18e-32 201.604
Metro 2 6.130 3.07e-06 4.503
Metro 5 9.729 5.7e-09 15.804
Metro 10 6.193 5.72e-06 19.535
Metro 15 5.786 1.4e-05 36.866
Metro 30 7.514 4.18e-07 103.664
DEMetro_Z 2 7.463 7.08e-08 4.291
DEMetro_Z 5 10.848 1.39e-09 150.467
DEMetro_Z 10 16.206 1.39e-12 229.434
DEMetro_Z 15 30.112 1.64e-17 283.035
DEMetro_Z 30 39.573 9.44e-20 265.721
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -5.114 6.16e-05 -1.144
DEMetro_Z_vs_SMC 1 -9.156 2.14e-08 -2.047
DEMetro_Z_vs_SMC 2 -1.637 0.118 -0.366
DEMetro_Z_vs_SMC 3 5.277 4.3e-05 1.180
DEMetro_Z_vs_SMC 4 9.064 2.5e-08 2.027
HMC_vs_Metro 0 -5.717 1.65e-05 -1.278
HMC_vs_Metro 1 -7.287 6.51e-07 -1.630
HMC_vs_Metro 2 -2.985 0.00761 -0.667
HMC_vs_Metro 3 -0.767 0.453 -0.171
HMC_vs_Metro 4 -2.877 0.00966 -0.643
Metro_vs_DEMetro_Z 0 0.216 0.831 0.048
Metro_vs_DEMetro_Z 1 -9.289 1.7e-08 -2.077
Metro_vs_DEMetro_Z 2 -13.898 2.09e-11 -3.108
Metro_vs_DEMetro_Z 3 -21.478 8.68e-15 -4.803
Metro_vs_DEMetro_Z 4 -11.287 7.24e-10 -2.524
HMC_vs_SMC 0 -6.926 1.33e-06 -1.549
HMC_vs_SMC 1 -58.440 6.54e-23 -13.067
HMC_vs_SMC 2 -106.544 7.51e-28 -23.824
HMC_vs_SMC 3 -15.027 5.33e-12 -3.360
HMC_vs_SMC 4 -9.012 2.73e-08 -2.015
Metro_vs_SMC 0 -4.968 8.55e-05 -1.111
Metro_vs_SMC 1 -50.063 1.21e-21 -11.194
Metro_vs_SMC 2 -57.062 1.03e-22 -12.759
Metro_vs_SMC 3 -31.660 6.63e-18 -7.079
Metro_vs_SMC 4 -7.198 7.75e-07 -1.610
HMC_vs_DEMetro_Z 0 -7.315 6.17e-07 -1.636
HMC_vs_DEMetro_Z 1 -10.424 2.68e-09 -2.331
HMC_vs_DEMetro_Z 2 -15.441 3.3e-12 -3.453
HMC_vs_DEMetro_Z 3 -13.985 1.87e-11 -3.127
HMC_vs_DEMetro_Z 4 -11.763 3.62e-10 -2.630
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.017 0.014 0.005 0.461
HMC 5 0.021 0.015 0.002 3.463
HMC 10 0.030 0.015 0.002 8.395
HMC 15 0.060 0.016 0.002 24.950
HMC 30 0.097 0.015 0.002 41.016
SMC 2 0.096 0.014 0.005 17.524
SMC 5 0.518 0.015 0.002 264.590
SMC 10 0.461 0.015 0.002 253.604
SMC 15 0.440 0.016 0.002 237.483
SMC 30 0.416 0.015 0.002 201.604
Metro 2 0.035 0.014 0.005 4.503
Metro 5 0.045 0.015 0.002 15.804
Metro 10 0.049 0.015 0.002 19.535
Metro 15 0.082 0.016 0.002 36.866
Metro 30 0.221 0.015 0.002 103.664
DEMetro_Z 2 0.034 0.014 0.005 4.291
DEMetro_Z 5 0.301 0.015 0.002 150.467
DEMetro_Z 10 0.419 0.015 0.002 229.434
DEMetro_Z 15 0.522 0.016 0.002 283.035
DEMetro_Z 30 0.544 0.015 0.002 265.721
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_high_Multimodality (Mixture, dimension, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.644 2.27e-06 25.405
HMC 5 3.216 0.00453 14.954
HMC 10 3.785 0.00125 25.600
HMC 15 3.503 0.00237 39.641
HMC 30 5.477 2.76e-05 64.979
SMC 2 0.458 0.649 0.158
SMC 5 -0.167 0.868 -0.049
SMC 10 -0.744 0.462 -0.200
SMC 15 1.180 0.248 0.627
SMC 30 0.985 0.334 0.570
Metro 2 5.906 1.08e-05 28.676
Metro 5 6.204 5.7e-06 26.861
Metro 10 4.850 0.00011 28.334
Metro 15 4.875 0.000105 48.921
Metro 30 5.265 4.4e-05 55.595
DEMetro_Z 2 5.637 1.92e-05 23.279
DEMetro_Z 5 9.584 1.02e-08 71.532
DEMetro_Z 10 15.352 3.63e-12 228.424
DEMetro_Z 15 22.303 4.33e-15 488.284
DEMetro_Z 30 39.511 1.04e-19 974.763
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.330 0.745 0.074
HMC_vs_DEMetro_Z 1 -6.606 2.54e-06 -1.477
HMC_vs_DEMetro_Z 2 -12.195 1.97e-10 -2.727
HMC_vs_DEMetro_Z 3 -19.454 5.26e-14 -4.350
HMC_vs_DEMetro_Z 4 -34.712 1.19e-18 -7.762
Metro_vs_SMC 0 5.882 1.15e-05 1.315
Metro_vs_SMC 1 6.185 6.07e-06 1.383
Metro_vs_SMC 2 4.864 0.000108 1.088
Metro_vs_SMC 3 4.761 0.000136 1.065
Metro_vs_SMC 4 5.289 4.18e-05 1.183
Metro_vs_DEMetro_Z 0 0.823 0.421 0.184
Metro_vs_DEMetro_Z 1 -5.615 2.05e-05 -1.256
Metro_vs_DEMetro_Z 2 -12.356 1.58e-10 -2.763
Metro_vs_DEMetro_Z 3 -24.410 8.28e-16 -5.458
Metro_vs_DEMetro_Z 4 -33.312 2.56e-18 -7.449
HMC_vs_Metro 0 -0.990 0.334 -0.221
HMC_vs_Metro 1 -2.635 0.0163 -0.589
HMC_vs_Metro 2 -0.478 0.638 -0.107
HMC_vs_Metro 3 -0.587 0.564 -0.131
HMC_vs_Metro 4 1.368 0.187 0.306
HMC_vs_SMC 0 6.516 3.06e-06 1.457
HMC_vs_SMC 1 3.243 0.00429 0.725
HMC_vs_SMC 2 3.828 0.00113 0.856
HMC_vs_SMC 3 3.477 0.00252 0.778
HMC_vs_SMC 4 5.426 3.1e-05 1.213
DEMetro_Z_vs_SMC 0 5.592 2.16e-05 1.250
DEMetro_Z_vs_SMC 1 9.498 1.2e-08 2.124
DEMetro_Z_vs_SMC 2 15.359 3.63e-12 3.434
DEMetro_Z_vs_SMC 3 22.306 4.34e-15 4.988
DEMetro_Z_vs_SMC 4 39.250 1.19e-19 8.777
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 1.683 0.090 0.063 25.405
HMC 5 0.623 0.053 0.038 14.954
HMC 10 0.674 0.044 0.025 25.600
HMC 15 0.526 0.036 0.012 39.641
HMC 30 0.505 0.032 0.007 64.979
SMC 2 0.100 0.090 0.063 0.158
SMC 5 0.051 0.053 0.038 -0.049
SMC 10 0.039 0.044 0.025 -0.200
SMC 15 0.044 0.036 0.012 0.627
SMC 30 0.036 0.032 0.007 0.570
Metro 2 1.889 0.090 0.063 28.676
Metro 5 1.076 0.053 0.038 26.861
Metro 10 0.741 0.044 0.025 28.334
Metro 15 0.640 0.036 0.012 48.921
Metro 30 0.437 0.032 0.007 55.595
DEMetro_Z 2 1.550 0.090 0.063 23.279
DEMetro_Z 5 2.778 0.053 0.038 71.532
DEMetro_Z 10 5.664 0.044 0.025 228.424
DEMetro_Z 15 6.064 0.036 0.012 488.284
DEMetro_Z 30 7.127 0.032 0.007 974.763
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.649 0.000174 48.701
HMC 5 2.594 0.0178 30.101
HMC 10 3.134 0.00547 97.239
HMC 15 2.989 0.00754 69.221
HMC 30 3.935 0.00089 100.923
SMC 2 1.069 0.292 0.356
SMC 5 0.938 0.355 0.262
SMC 10 0.669 0.508 0.281
SMC 15 0.573 0.57 0.173
SMC 30 1.101 0.28 0.531
Metro 2 4.160 0.000532 66.116
Metro 5 3.834 0.00112 51.672
Metro 10 3.510 0.00234 95.001
Metro 15 3.519 0.00229 78.107
Metro 30 3.648 0.00171 77.196
DEMetro_Z 2 3.307 0.00371 42.920
DEMetro_Z 5 9.182 2.04e-08 478.093
DEMetro_Z 10 17.276 4.48e-13 3429.162
DEMetro_Z 15 17.271 4.5e-13 4097.380
DEMetro_Z 30 29.267 2.87e-17 7549.873
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 4.595 0.000198 1.027
HMC_vs_SMC 1 2.564 0.019 0.573
HMC_vs_SMC 2 3.113 0.00573 0.696
HMC_vs_SMC 3 2.973 0.00782 0.665
HMC_vs_SMC 4 3.938 0.000883 0.881
Metro_vs_DEMetro_Z 0 1.078 0.294 0.241
Metro_vs_DEMetro_Z 1 -7.659 3.18e-07 -1.713
Metro_vs_DEMetro_Z 2 -16.166 1.46e-12 -3.615
Metro_vs_DEMetro_Z 3 -17.333 4.22e-13 -3.876
Metro_vs_DEMetro_Z 4 -29.147 3.1e-17 -6.518
HMC_vs_Metro 0 -1.430 0.169 -0.320
HMC_vs_Metro 1 -1.913 0.071 -0.428
HMC_vs_Metro 2 0.083 0.935 0.019
HMC_vs_Metro 3 -0.252 0.803 -0.056
HMC_vs_Metro 4 1.673 0.111 0.374
HMC_vs_DEMetro_Z 0 0.304 0.765 0.068
HMC_vs_DEMetro_Z 1 -7.950 1.84e-07 -1.778
HMC_vs_DEMetro_Z 2 -15.506 3.07e-12 -3.467
HMC_vs_DEMetro_Z 3 -17.075 5.52e-13 -3.818
HMC_vs_DEMetro_Z 4 -29.446 2.56e-17 -6.584
Metro_vs_SMC 0 4.139 0.000558 0.926
Metro_vs_SMC 1 3.806 0.00119 0.851
Metro_vs_SMC 2 3.483 0.00249 0.779
Metro_vs_SMC 3 3.505 0.00237 0.784
Metro_vs_SMC 4 3.639 0.00175 0.814
DEMetro_Z_vs_SMC 0 3.279 0.00395 0.733
DEMetro_Z_vs_SMC 1 9.190 2.01e-08 2.055
DEMetro_Z_vs_SMC 2 17.266 4.53e-13 3.861
DEMetro_Z_vs_SMC 3 17.268 4.52e-13 3.861
DEMetro_Z_vs_SMC 4 29.280 2.84e-17 6.547
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 5.741 0.121 0.115 48.701
HMC 5 2.269 0.091 0.072 30.101
HMC 10 3.144 0.070 0.032 97.239
HMC 15 2.490 0.067 0.035 69.221
HMC 30 2.159 0.056 0.021 100.923
SMC 2 0.162 0.121 0.115 0.356
SMC 5 0.110 0.091 0.072 0.262
SMC 10 0.079 0.070 0.032 0.281
SMC 15 0.074 0.067 0.035 0.173
SMC 30 0.067 0.056 0.021 0.531
Metro 2 7.751 0.121 0.115 66.116
Metro 5 3.830 0.091 0.072 51.672
Metro 10 3.073 0.070 0.032 95.001
Metro 15 2.801 0.067 0.035 78.107
Metro 30 1.665 0.056 0.021 77.196
DEMetro_Z 2 5.074 0.121 0.115 42.920
DEMetro_Z 5 34.689 0.091 0.072 478.093
DEMetro_Z 10 108.491 0.070 0.032 3429.162
DEMetro_Z 15 143.442 0.067 0.035 4097.380
DEMetro_Z 30 157.410 0.056 0.021 7549.873
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.812 1.61e-06 26.403
HMC 5 3.278 0.00394 15.389
HMC 10 3.710 0.00148 29.181
HMC 15 3.532 0.00223 49.376
HMC 30 5.377 3.44e-05 83.768
SMC 2 0.162 0.872 0.055
SMC 5 -0.197 0.845 -0.056
SMC 10 -0.655 0.517 -0.172
SMC 15 1.306 0.203 0.738
SMC 30 1.321 0.199 0.815
Metro 2 5.844 1.23e-05 30.230
Metro 5 5.987 9.04e-06 27.159
Metro 10 4.878 0.000104 31.904
Metro 15 4.805 0.000123 60.840
Metro 30 5.213 4.95e-05 71.305
DEMetro_Z 2 5.620 1.99e-05 25.073
DEMetro_Z 5 12.645 1.05e-10 111.775
DEMetro_Z 10 29.281 2.81e-17 444.902
DEMetro_Z 15 30.090 1.71e-17 1122.650
DEMetro_Z 30 71.902 1.29e-24 2174.952
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.736 0.471 0.165
Metro_vs_DEMetro_Z 1 -8.737 4.42e-08 -1.954
Metro_vs_DEMetro_Z 2 -24.794 6.21e-16 -5.544
Metro_vs_DEMetro_Z 3 -31.855 5.91e-18 -7.123
Metro_vs_DEMetro_Z 4 -63.566 1.33e-23 -14.214
DEMetro_Z_vs_SMC 0 5.592 2.16e-05 1.250
DEMetro_Z_vs_SMC 1 12.531 1.24e-10 2.802
DEMetro_Z_vs_SMC 2 29.354 2.71e-17 6.564
DEMetro_Z_vs_SMC 3 30.049 1.76e-17 6.719
DEMetro_Z_vs_SMC 4 71.489 1.45e-24 15.985
HMC_vs_DEMetro_Z 0 0.197 0.846 0.044
HMC_vs_DEMetro_Z 1 -9.419 1.37e-08 -2.106
HMC_vs_DEMetro_Z 2 -21.803 6.59e-15 -4.875
HMC_vs_DEMetro_Z 3 -28.324 5.27e-17 -6.333
HMC_vs_DEMetro_Z 4 -68.088 3.64e-24 -15.225
HMC_vs_Metro 0 -1.081 0.293 -0.242
HMC_vs_Metro 1 -2.442 0.0246 -0.546
HMC_vs_Metro 2 -0.393 0.698 -0.088
HMC_vs_Metro 3 -0.584 0.566 -0.131
HMC_vs_Metro 4 1.303 0.208 0.291
HMC_vs_SMC 0 6.756 1.87e-06 1.511
HMC_vs_SMC 1 3.293 0.00382 0.736
HMC_vs_SMC 2 3.737 0.0014 0.836
HMC_vs_SMC 3 3.508 0.00235 0.785
HMC_vs_SMC 4 5.323 3.88e-05 1.190
Metro_vs_SMC 0 5.859 1.21e-05 1.310
Metro_vs_SMC 1 5.977 9.42e-06 1.337
Metro_vs_SMC 2 4.884 0.000103 1.092
Metro_vs_SMC 3 4.701 0.000155 1.051
Metro_vs_SMC 4 5.224 4.83e-05 1.168
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 1.504 0.099 0.053 26.403
HMC 5 0.536 0.061 0.031 15.389
HMC 10 0.557 0.050 0.017 29.181
HMC 15 0.430 0.044 0.008 49.376
HMC 30 0.416 0.039 0.004 83.768
SMC 2 0.102 0.099 0.053 0.055
SMC 5 0.059 0.061 0.031 -0.056
SMC 10 0.047 0.050 0.017 -0.172
SMC 15 0.050 0.044 0.008 0.738
SMC 30 0.043 0.039 0.004 0.815
Metro 2 1.708 0.099 0.053 30.230
Metro 5 0.900 0.061 0.031 27.159
Metro 10 0.604 0.050 0.017 31.904
Metro 15 0.519 0.044 0.008 60.840
Metro 30 0.360 0.039 0.004 71.305
DEMetro_Z 2 1.434 0.099 0.053 25.073
DEMetro_Z 5 3.512 0.061 0.031 111.775
DEMetro_Z 10 7.775 0.050 0.017 444.902
DEMetro_Z 15 8.811 0.044 0.008 1122.650
DEMetro_Z 30 9.823 0.039 0.004 2174.952
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.859 1.48e-06 31.431
HMC 5 3.247 0.00423 16.635
HMC 10 3.822 0.00115 28.954
HMC 15 3.521 0.00228 47.252
HMC 30 5.370 3.49e-05 75.768
SMC 2 0.627 0.534 0.228
SMC 5 -0.458 0.65 -0.128
SMC 10 -0.586 0.562 -0.155
SMC 15 1.150 0.261 0.667
SMC 30 1.168 0.254 0.666
Metro 2 6.136 6.64e-06 35.125
Metro 5 6.261 5.08e-06 29.829
Metro 10 4.865 0.000107 32.368
Metro 15 4.836 0.000115 58.879
Metro 30 5.236 4.69e-05 64.666
DEMetro_Z 2 5.829 1.27e-05 28.812
DEMetro_Z 5 17.526 2.82e-13 52.519
DEMetro_Z 10 52.181 1.47e-22 89.151
DEMetro_Z 15 48.400 1.63e-21 158.357
DEMetro_Z 30 54.095 2.25e-22 224.943
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.775 1.45e-05 1.291
DEMetro_Z_vs_SMC 1 17.222 4.74e-13 3.851
DEMetro_Z_vs_SMC 2 52.056 5.82e-22 11.640
DEMetro_Z_vs_SMC 3 48.122 2.56e-21 10.760
DEMetro_Z_vs_SMC 4 55.605 1.67e-22 12.434
HMC_vs_Metro 0 -0.978 0.341 -0.219
HMC_vs_Metro 1 -2.686 0.0146 -0.601
HMC_vs_Metro 2 -0.517 0.611 -0.116
HMC_vs_Metro 3 -0.608 0.55 -0.136
HMC_vs_Metro 4 1.334 0.198 0.298
Metro_vs_DEMetro_Z 0 0.815 0.425 0.182
Metro_vs_DEMetro_Z 1 -4.460 0.000269 -0.997
Metro_vs_DEMetro_Z 2 -8.205 1.15e-07 -1.835
Metro_vs_DEMetro_Z 3 -8.780 4.1e-08 -1.963
Metro_vs_DEMetro_Z 4 -12.484 1.32e-10 -2.792
HMC_vs_SMC 0 6.735 1.95e-06 1.506
HMC_vs_SMC 1 3.276 0.00397 0.733
HMC_vs_SMC 2 3.848 0.00108 0.861
HMC_vs_SMC 3 3.501 0.00239 0.783
HMC_vs_SMC 4 5.317 3.94e-05 1.189
Metro_vs_SMC 0 6.117 7.01e-06 1.368
Metro_vs_SMC 1 6.269 5.1e-06 1.402
Metro_vs_SMC 2 4.864 0.000108 1.088
Metro_vs_SMC 3 4.725 0.000147 1.057
Metro_vs_SMC 4 5.248 4.58e-05 1.174
HMC_vs_DEMetro_Z 0 0.343 0.736 0.077
HMC_vs_DEMetro_Z 1 -6.092 7.4e-06 -1.362
HMC_vs_DEMetro_Z 2 -7.541 3.98e-07 -1.686
HMC_vs_DEMetro_Z 3 -7.931 1.91e-07 -1.773
HMC_vs_DEMetro_Z 4 -9.633 9.58e-09 -2.154
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.255 0.013 0.008 31.431
HMC 5 0.143 0.012 0.008 16.635
HMC 10 0.201 0.014 0.006 28.954
HMC 15 0.179 0.013 0.004 47.252
HMC 30 0.206 0.014 0.003 75.768
SMC 2 0.015 0.013 0.008 0.228
SMC 5 0.011 0.012 0.008 -0.128
SMC 10 0.013 0.014 0.006 -0.155
SMC 15 0.016 0.013 0.004 0.667
SMC 30 0.016 0.014 0.003 0.666
Metro 2 0.284 0.013 0.008 35.125
Metro 5 0.247 0.012 0.008 29.829
Metro 10 0.223 0.014 0.006 32.368
Metro 15 0.220 0.013 0.004 58.879
Metro 30 0.178 0.014 0.003 64.666
DEMetro_Z 2 0.235 0.013 0.008 28.812
DEMetro_Z 5 0.425 0.012 0.008 52.519
DEMetro_Z 10 0.590 0.014 0.006 89.151
DEMetro_Z 15 0.569 0.013 0.004 158.357
DEMetro_Z 30 0.582 0.014 0.003 224.943
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 197.060 3.02e-58 65.947
HMC 5 190.197 1.94e-55 69.254
HMC 10 211.207 7.89e-58 75.109
HMC 15 204.415 7.68e-42 122.262
HMC 30 208.776 1.26e-39 145.646
SMC 2 -0.701 0.488 -0.220
SMC 5 0.946 0.35 0.314
SMC 10 0.738 0.465 0.234
SMC 15 1.215 0.234 0.577
SMC 30 -0.050 0.961 -0.021
Metro 2 17.061 4.87e-13 61.044
Metro 5 13.422 3.57e-11 60.706
Metro 10 16.420 1e-12 67.335
Metro 15 13.509 3.34e-11 106.687
Metro 30 80.291 3.66e-26 143.223
DEMetro_Z 2 5.681 1.76e-05 39.922
DEMetro_Z 5 15.809 2.01e-12 73.466
DEMetro_Z 10 12.481 1.33e-10 344.591
DEMetro_Z 15 17.818 2.57e-13 747.161
DEMetro_Z 30 20.390 2.24e-14 1555.508
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 3.699 0.00152 0.827
HMC_vs_DEMetro_Z 1 -0.908 0.375 -0.203
HMC_vs_DEMetro_Z 2 -9.732 8.14e-09 -2.176
HMC_vs_DEMetro_Z 3 -14.840 6.65e-12 -3.318
HMC_vs_DEMetro_Z 4 -18.500 1.31e-13 -4.137
Metro_vs_SMC 0 17.377 4.03e-13 3.886
Metro_vs_SMC 1 13.333 4.29e-11 2.981
Metro_vs_SMC 2 16.308 1.25e-12 3.647
Metro_vs_SMC 3 13.277 4.61e-11 2.969
Metro_vs_SMC 4 80.209 1.63e-25 17.935
Metro_vs_DEMetro_Z 0 2.829 0.0107 0.633
Metro_vs_DEMetro_Z 1 -2.775 0.0121 -0.620
Metro_vs_DEMetro_Z 2 -10.097 4.5e-09 -2.258
Metro_vs_DEMetro_Z 3 -15.018 5.39e-12 -3.358
Metro_vs_DEMetro_Z 4 -18.405 1.44e-13 -4.115
HMC_vs_Metro 0 1.366 0.188 0.305
HMC_vs_Metro 1 1.895 0.0734 0.424
HMC_vs_Metro 2 1.920 0.0699 0.429
HMC_vs_Metro 3 2.020 0.0578 0.452
HMC_vs_Metro 4 1.419 0.172 0.317
HMC_vs_SMC 0 156.552 5.05e-31 35.006
HMC_vs_SMC 1 240.797 1.42e-34 53.844
HMC_vs_SMC 2 190.852 1.17e-32 42.676
HMC_vs_SMC 3 154.056 6.85e-31 34.448
HMC_vs_SMC 4 183.717 2.42e-32 41.080
DEMetro_Z_vs_SMC 0 5.709 1.67e-05 1.277
DEMetro_Z_vs_SMC 1 15.693 2.48e-12 3.509
DEMetro_Z_vs_SMC 2 12.443 1.4e-10 2.782
DEMetro_Z_vs_SMC 3 17.792 2.64e-13 3.978
DEMetro_Z_vs_SMC 4 20.408 2.21e-14 4.563
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 4.226 0.090 0.063 65.947
HMC 5 2.692 0.053 0.038 69.254
HMC 10 1.892 0.044 0.025 75.109
HMC 15 1.546 0.036 0.012 122.262
HMC 30 1.092 0.032 0.007 145.646
SMC 2 0.076 0.090 0.063 -0.220
SMC 5 0.065 0.053 0.038 0.314
SMC 10 0.049 0.044 0.025 0.234
SMC 15 0.043 0.036 0.012 0.577
SMC 30 0.032 0.032 0.007 -0.021
Metro 2 3.919 0.090 0.063 61.044
Metro 5 2.366 0.053 0.038 60.706
Metro 10 1.700 0.044 0.025 67.335
Metro 15 1.353 0.036 0.012 106.687
Metro 30 1.075 0.032 0.007 143.223
DEMetro_Z 2 2.594 0.090 0.063 39.922
DEMetro_Z 5 2.852 0.053 0.038 73.466
DEMetro_Z 10 8.522 0.044 0.025 344.591
DEMetro_Z 15 9.260 0.036 0.012 747.161
DEMetro_Z 30 11.354 0.032 0.007 1555.508
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 643.357 5.51e-77 219.494
HMC 5 704.742 8.24e-80 221.169
HMC 10 614.225 1.73e-54 357.528
HMC 15 644.972 8.6e-69 263.366
HMC 30 697.483 2.22e-65 312.559
SMC 2 0.110 0.913 0.029
SMC 5 -0.865 0.394 -0.228
SMC 10 1.856 0.0714 0.643
SMC 15 0.169 0.867 0.058
SMC 30 -1.338 0.189 -0.416
Metro 2 14.204 1.42e-11 199.259
Metro 5 10.866 1.35e-09 186.363
Metro 10 12.276 1.76e-10 305.653
Metro 15 10.539 2.24e-09 218.630
Metro 30 49.448 1.39e-21 303.396
DEMetro_Z 2 5.291 4.17e-05 126.767
DEMetro_Z 5 6.680 2.19e-06 254.436
DEMetro_Z 10 11.101 9.54e-10 743.207
DEMetro_Z 15 12.378 1.53e-10 758.119
DEMetro_Z 30 15.997 1.76e-12 1014.149
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 737.286 8.31e-44 164.862
HMC_vs_SMC 1 906.600 1.64e-45 202.722
HMC_vs_SMC 2 627.792 1.76e-42 140.379
HMC_vs_SMC 3 793.478 2.06e-44 177.427
HMC_vs_SMC 4 914.637 1.38e-45 204.519
Metro_vs_DEMetro_Z 0 2.694 0.0144 0.602
Metro_vs_DEMetro_Z 1 -1.868 0.0772 -0.418
Metro_vs_DEMetro_Z 2 -6.749 1.9e-06 -1.509
Metro_vs_DEMetro_Z 3 -7.457 4.68e-07 -1.668
Metro_vs_DEMetro_Z 4 -11.145 8.93e-10 -2.492
HMC_vs_Metro 0 1.451 0.163 0.324
HMC_vs_Metro 1 2.028 0.0568 0.453
HMC_vs_Metro 2 2.093 0.05 0.468
HMC_vs_Metro 3 2.154 0.0443 0.482
HMC_vs_Metro 4 1.468 0.158 0.328
HMC_vs_DEMetro_Z 0 3.874 0.00102 0.866
HMC_vs_DEMetro_Z 1 -0.873 0.394 -0.195
HMC_vs_DEMetro_Z 2 -5.757 1.51e-05 -1.287
HMC_vs_DEMetro_Z 3 -8.075 1.46e-07 -1.806
HMC_vs_DEMetro_Z 4 -11.045 1.04e-09 -2.470
Metro_vs_SMC 0 14.209 1.42e-11 3.177
Metro_vs_SMC 1 10.870 1.35e-09 2.431
Metro_vs_SMC 2 12.280 1.75e-10 2.746
Metro_vs_SMC 3 10.483 2.45e-09 2.344
Metro_vs_SMC 4 49.801 1.34e-21 11.136
DEMetro_Z_vs_SMC 0 5.282 4.25e-05 1.181
DEMetro_Z_vs_SMC 1 6.693 2.13e-06 1.497
DEMetro_Z_vs_SMC 2 11.094 9.64e-10 2.481
DEMetro_Z_vs_SMC 3 12.380 1.53e-10 2.768
DEMetro_Z_vs_SMC 4 15.989 1.78e-12 3.575
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 25.451 0.121 0.115 219.494
HMC 5 16.096 0.091 0.072 221.169
HMC 10 11.374 0.070 0.032 357.528
HMC 15 9.283 0.067 0.035 263.366
HMC 30 6.570 0.056 0.021 312.559
SMC 2 0.124 0.121 0.115 0.029
SMC 5 0.075 0.091 0.072 -0.228
SMC 10 0.090 0.070 0.032 0.643
SMC 15 0.070 0.067 0.035 0.058
SMC 30 0.047 0.056 0.021 -0.416
Metro 2 23.116 0.121 0.115 199.259
Metro 5 13.577 0.091 0.072 186.363
Metro 10 9.734 0.070 0.032 305.653
Metro 15 7.718 0.067 0.035 218.630
Metro 30 6.379 0.056 0.021 303.396
DEMetro_Z 2 14.750 0.121 0.115 126.767
DEMetro_Z 5 18.504 0.091 0.072 254.436
DEMetro_Z 10 23.568 0.070 0.032 743.207
DEMetro_Z 15 26.595 0.067 0.035 758.119
DEMetro_Z 30 21.193 0.056 0.021 1014.149
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 53.435 3.35e-23 69.187
HMC 5 40.196 2.47e-20 69.759
HMC 10 59.687 5.44e-24 84.236
HMC 15 79.607 5.45e-26 154.477
HMC 30 81.149 5.29e-26 184.720
SMC 2 -0.877 0.386 -0.263
SMC 5 0.502 0.619 0.153
SMC 10 0.717 0.478 0.229
SMC 15 1.235 0.227 0.596
SMC 30 0.102 0.919 0.045
Metro 2 16.036 1.53e-12 65.963
Metro 5 13.222 4.64e-11 60.684
Metro 10 16.088 1.48e-12 77.564
Metro 15 13.126 5.54e-11 133.667
Metro 30 55.746 1.12e-22 186.353
DEMetro_Z 2 5.676 1.79e-05 44.051
DEMetro_Z 5 16.051 1.56e-12 82.015
DEMetro_Z 10 13.288 4.54e-11 419.126
DEMetro_Z 15 17.739 2.78e-13 994.365
DEMetro_Z 30 21.984 5.67e-15 2086.007
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 2.670 0.0151 0.597
Metro_vs_DEMetro_Z 1 -4.037 0.000704 -0.903
Metro_vs_DEMetro_Z 2 -10.790 1.53e-09 -2.413
Metro_vs_DEMetro_Z 3 -15.128 4.74e-12 -3.383
Metro_vs_DEMetro_Z 4 -19.800 3.82e-14 -4.427
DEMetro_Z_vs_SMC 0 5.707 1.68e-05 1.276
DEMetro_Z_vs_SMC 1 16.033 1.7e-12 3.585
DEMetro_Z_vs_SMC 2 13.265 4.68e-11 2.966
DEMetro_Z_vs_SMC 3 17.718 2.85e-13 3.962
DEMetro_Z_vs_SMC 4 21.999 5.6e-15 4.919
HMC_vs_DEMetro_Z 0 3.086 0.00608 0.690
HMC_vs_DEMetro_Z 1 -2.190 0.0412 -0.490
HMC_vs_DEMetro_Z 2 -10.673 1.83e-09 -2.386
HMC_vs_DEMetro_Z 3 -14.814 6.85e-12 -3.313
HMC_vs_DEMetro_Z 4 -19.954 3.32e-14 -4.462
HMC_vs_Metro 0 0.712 0.485 0.159
HMC_vs_Metro 1 2.091 0.0502 0.467
HMC_vs_Metro 2 1.487 0.153 0.333
HMC_vs_Metro 3 2.079 0.0514 0.465
HMC_vs_Metro 4 -0.452 0.656 -0.101
HMC_vs_SMC 0 52.095 5.73e-22 11.649
HMC_vs_SMC 1 40.691 6.02e-20 9.099
HMC_vs_SMC 2 57.706 8.31e-23 12.903
HMC_vs_SMC 3 81.002 1.36e-25 18.113
HMC_vs_SMC 4 82.107 1.05e-25 18.360
Metro_vs_SMC 0 16.318 1.24e-12 3.649
Metro_vs_SMC 1 13.244 4.82e-11 2.961
Metro_vs_SMC 2 16.050 1.67e-12 3.589
Metro_vs_SMC 3 12.949 7.09e-11 2.896
Metro_vs_SMC 4 54.603 2.36e-22 12.210
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 3.781 0.099 0.053 69.187
HMC 5 2.215 0.061 0.031 69.759
HMC 10 1.513 0.050 0.017 84.236
HMC 15 1.250 0.044 0.008 154.477
HMC 30 0.870 0.039 0.004 184.720
SMC 2 0.085 0.099 0.053 -0.263
SMC 5 0.066 0.061 0.031 0.153
SMC 10 0.054 0.050 0.017 0.229
SMC 15 0.049 0.044 0.008 0.596
SMC 30 0.039 0.039 0.004 0.045
Metro 2 3.610 0.099 0.053 65.963
Metro 5 1.935 0.061 0.031 60.684
Metro 10 1.397 0.050 0.017 77.564
Metro 15 1.088 0.044 0.008 133.667
Metro 30 0.877 0.039 0.004 186.353
DEMetro_Z 2 2.444 0.099 0.053 44.051
DEMetro_Z 5 2.593 0.061 0.031 82.015
DEMetro_Z 10 7.327 0.050 0.017 419.126
DEMetro_Z 15 7.810 0.044 0.008 994.365
DEMetro_Z 30 9.422 0.039 0.004 2086.007
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 130.607 5.03e-37 77.892
HMC 5 125.468 1.23e-36 74.602
HMC 10 176.031 3.78e-45 84.638
HMC 15 135.760 5.13e-32 146.691
HMC 30 130.344 7.15e-31 175.605
SMC 2 -0.501 0.619 -0.166
SMC 5 0.825 0.414 0.267
SMC 10 0.671 0.506 0.212
SMC 15 1.346 0.189 0.658
SMC 30 0.067 0.947 0.029
Metro 2 17.456 3.34e-13 72.730
Metro 5 13.559 3.02e-11 65.674
Metro 10 16.522 9.14e-13 75.343
Metro 15 13.414 3.81e-11 130.233
Metro 30 66.221 3.23e-24 170.881
DEMetro_Z 2 5.750 1.52e-05 48.403
DEMetro_Z 5 20.746 1.28e-14 61.159
DEMetro_Z 10 41.599 2.77e-20 127.923
DEMetro_Z 15 76.929 2.35e-25 251.636
DEMetro_Z 30 43.158 1.9e-20 367.497
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.770 1.47e-05 1.290
DEMetro_Z_vs_SMC 1 20.736 1.65e-14 4.637
DEMetro_Z_vs_SMC 2 40.771 5.8e-20 9.117
DEMetro_Z_vs_SMC 3 72.733 1.04e-24 16.264
DEMetro_Z_vs_SMC 4 43.617 1.63e-20 9.753
HMC_vs_Metro 0 1.227 0.235 0.274
HMC_vs_Metro 1 1.772 0.0924 0.396
HMC_vs_Metro 2 2.033 0.0563 0.455
HMC_vs_Metro 3 1.696 0.106 0.379
HMC_vs_Metro 4 1.602 0.126 0.358
Metro_vs_DEMetro_Z 0 2.730 0.0133 0.610
Metro_vs_DEMetro_Z 1 0.859 0.401 0.192
Metro_vs_DEMetro_Z 2 -8.860 3.56e-08 -1.981
Metro_vs_DEMetro_Z 3 -12.761 9.1e-11 -2.854
Metro_vs_DEMetro_Z 4 -21.077 1.22e-14 -4.713
HMC_vs_SMC 0 114.037 2.07e-28 25.499
HMC_vs_SMC 1 116.069 1.48e-28 25.954
HMC_vs_SMC 2 173.083 7.51e-32 38.703
HMC_vs_SMC 3 129.817 1.77e-29 29.028
HMC_vs_SMC 4 126.424 2.92e-29 28.269
Metro_vs_SMC 0 17.729 2.81e-13 3.964
Metro_vs_SMC 1 13.476 3.56e-11 3.013
Metro_vs_SMC 2 16.478 1.04e-12 3.685
Metro_vs_SMC 3 13.178 5.25e-11 2.947
Metro_vs_SMC 4 67.616 4.15e-24 15.119
HMC_vs_DEMetro_Z 0 3.470 0.00256 0.776
HMC_vs_DEMetro_Z 1 4.830 0.000116 1.080
HMC_vs_DEMetro_Z 2 -14.118 1.59e-11 -3.157
HMC_vs_DEMetro_Z 3 -26.365 1.99e-16 -5.895
HMC_vs_DEMetro_Z 4 -22.851 2.79e-15 -5.110
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.614 0.013 0.008 77.892
HMC 5 0.599 0.012 0.008 74.602
HMC 10 0.561 0.014 0.006 84.638
HMC 15 0.528 0.013 0.004 146.691
HMC 30 0.458 0.014 0.003 175.605
SMC 2 0.012 0.013 0.008 -0.166
SMC 5 0.014 0.012 0.008 0.267
SMC 10 0.015 0.014 0.006 0.212
SMC 15 0.016 0.013 0.004 0.658
SMC 30 0.014 0.014 0.003 0.029
Metro 2 0.574 0.013 0.008 72.730
Metro 5 0.529 0.012 0.008 65.674
Metro 10 0.501 0.014 0.006 75.343
Metro 15 0.470 0.013 0.004 130.233
Metro 30 0.446 0.014 0.003 170.881
DEMetro_Z 2 0.386 0.013 0.008 48.403
DEMetro_Z 5 0.493 0.012 0.008 61.159
DEMetro_Z 10 0.841 0.014 0.006 127.923
DEMetro_Z 15 0.896 0.013 0.004 251.636
DEMetro_Z 30 0.942 0.014 0.003 367.497
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_heavy_Tails_and_high_correlation (MvStudentT, dimension, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.131 0.896 0.037
HMC 5 2.429 0.0216 1.159
HMC 10 1.764 0.0917 1.505
HMC 15 3.594 0.00141 2.185
HMC 30 4.108 0.000549 5.924
SMC 2 2.523 0.0167 1.033
SMC 5 7.022 1.07e-06 33.637
SMC 10 8.622 4.57e-08 18.623
SMC 15 5.945 1e-05 53.656
SMC 30 38.681 1.49e-19 336.521
Metro 2 1.892 0.0733 3.251
Metro 5 7.032 9.36e-07 14.151
Metro 10 3.241 0.00427 11.946
Metro 15 4.351 0.000344 139.579
Metro 30 4.059 0.00067 739.086
DEMetro_Z 2 2.751 0.0102 1.322
DEMetro_Z 5 4.438 0.000282 339.261
DEMetro_Z 10 6.562 2.77e-06 100.019
DEMetro_Z 15 6.316 4.62e-06 494.912
DEMetro_Z 30 10.415 2.72e-09 1257.395
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.768 0.0123 -0.619
HMC_vs_DEMetro_Z 1 -4.418 0.000295 -0.988
HMC_vs_DEMetro_Z 2 -6.381 4.03e-06 -1.427
HMC_vs_DEMetro_Z 3 -6.282 4.96e-06 -1.405
HMC_vs_DEMetro_Z 4 -10.318 3.17e-09 -2.307
Metro_vs_SMC 0 1.190 0.249 0.266
Metro_vs_SMC 1 -4.711 0.000152 -1.053
Metro_vs_SMC 2 -1.544 0.139 -0.345
Metro_vs_SMC 3 2.785 0.0118 0.623
Metro_vs_SMC 4 2.204 0.0401 0.493
Metro_vs_DEMetro_Z 0 1.129 0.273 0.253
Metro_vs_DEMetro_Z 1 -4.259 0.000424 -0.952
Metro_vs_DEMetro_Z 2 -5.887 1.14e-05 -1.316
Metro_vs_DEMetro_Z 3 -4.181 0.000507 -0.935
Metro_vs_DEMetro_Z 4 -2.072 0.0521 -0.463
HMC_vs_Metro 0 -1.817 0.0851 -0.406
HMC_vs_Metro 1 -6.576 2.7e-06 -1.470
HMC_vs_Metro 2 -3.021 0.00702 -0.676
HMC_vs_Metro 3 -4.310 0.000377 -0.964
HMC_vs_Metro 4 -4.040 0.0007 -0.903
HMC_vs_SMC 0 -3.591 0.00195 -0.803
HMC_vs_SMC 1 -6.683 2.17e-06 -1.494
HMC_vs_SMC 2 -7.062 1.01e-06 -1.579
HMC_vs_SMC 3 -5.823 1.31e-05 -1.302
HMC_vs_SMC 4 -36.086 5.74e-19 -8.069
DEMetro_Z_vs_SMC 0 0.504 0.62 0.113
DEMetro_Z_vs_SMC 1 4.028 0.000718 0.901
DEMetro_Z_vs_SMC 2 4.925 9.4e-05 1.101
DEMetro_Z_vs_SMC 3 5.694 1.73e-05 1.273
DEMetro_Z_vs_SMC 4 7.570 3.77e-07 1.693
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.069 0.067 0.049 0.037
HMC 5 0.092 0.052 0.035 1.159
HMC 10 0.247 0.082 0.109 1.505
HMC 15 0.139 0.056 0.038 2.185
HMC 30 0.286 0.062 0.038 5.924
SMC 2 0.117 0.067 0.049 1.033
SMC 5 1.215 0.052 0.035 33.637
SMC 10 2.120 0.082 0.109 18.623
SMC 15 2.117 0.056 0.038 53.656
SMC 30 12.789 0.062 0.038 336.521
Metro 2 0.225 0.067 0.049 3.251
Metro 5 0.542 0.052 0.035 14.151
Metro 10 1.389 0.082 0.109 11.946
Metro 15 5.417 0.056 0.038 139.579
Metro 30 28.013 0.062 0.038 739.086
DEMetro_Z 2 0.131 0.067 0.049 1.322
DEMetro_Z 5 11.785 0.052 0.035 339.261
DEMetro_Z 10 11.026 0.082 0.109 100.019
DEMetro_Z 15 19.066 0.056 0.038 494.912
DEMetro_Z 30 47.614 0.062 0.038 1257.395
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.007 0.324 -0.242
HMC 5 1.486 0.148 0.675
HMC 10 -0.656 0.518 -0.161
HMC 15 -0.099 0.922 -0.027
HMC 30 1.007 0.323 0.515
SMC 2 1.851 0.0742 0.474
SMC 5 22.567 3.46e-15 300.331
SMC 10 26.521 5.3e-18 6.135
SMC 15 145.779 5.83e-31 319.542
SMC 30 132.805 5.63e-30 372.997
Metro 2 0.054 0.957 0.016
Metro 5 1.171 0.249 0.353
Metro 10 -0.320 0.751 -0.082
Metro 15 1.409 0.175 70.849
Metro 30 2.223 0.0385 664.387
DEMetro_Z 2 -0.775 0.446 -0.183
DEMetro_Z 5 3.678 0.0016 462.934
DEMetro_Z 10 6.160 7.44e-07 2.651
DEMetro_Z 15 5.445 2.97e-05 148.367
DEMetro_Z 30 13.798 2.35e-11 178.019
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -4.571 0.000209 -1.022
HMC_vs_SMC 1 -22.368 4.13e-15 -5.002
HMC_vs_SMC 2 -52.021 5.89e-22 -11.632
HMC_vs_SMC 3 -146.746 1.72e-30 -32.813
HMC_vs_SMC 4 -121.894 5.84e-29 -27.256
Metro_vs_DEMetro_Z 0 1.056 0.304 0.236
Metro_vs_DEMetro_Z 1 -3.676 0.0016 -0.822
Metro_vs_DEMetro_Z 2 -8.272 1.02e-07 -1.850
Metro_vs_DEMetro_Z 3 -1.376 0.185 -0.308
Metro_vs_DEMetro_Z 4 1.656 0.114 0.370
HMC_vs_Metro 0 -1.392 0.18 -0.311
HMC_vs_Metro 1 0.777 0.447 0.174
HMC_vs_Metro 2 -0.516 0.612 -0.115
HMC_vs_Metro 3 -1.411 0.174 -0.315
HMC_vs_Metro 4 -2.222 0.0386 -0.497
HMC_vs_DEMetro_Z 0 -2.402 0.0267 -0.537
HMC_vs_DEMetro_Z 1 -3.674 0.00161 -0.821
HMC_vs_DEMetro_Z 2 -7.104 9.33e-07 -1.589
HMC_vs_DEMetro_Z 3 -5.436 3.03e-05 -1.216
HMC_vs_DEMetro_Z 4 -13.752 2.51e-11 -3.075
Metro_vs_SMC 0 -1.944 0.0669 -0.435
Metro_vs_SMC 1 -22.436 3.9e-15 -5.017
Metro_vs_SMC 2 -38.894 1.41e-19 -8.697
Metro_vs_SMC 3 -4.980 8.31e-05 -1.114
Metro_vs_SMC 4 0.975 0.342 0.218
DEMetro_Z_vs_SMC 0 -4.255 0.000428 -0.952
DEMetro_Z_vs_SMC 1 1.309 0.206 0.293
DEMetro_Z_vs_SMC 2 -9.436 1.33e-08 -2.110
DEMetro_Z_vs_SMC 3 -6.465 3.39e-06 -1.446
DEMetro_Z_vs_SMC 4 -14.620 8.64e-12 -3.269
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 4.763 8.853 16.927 -0.242
HMC 5 7.213 3.438 5.591 0.675
HMC 10 26.639 61.875 219.151 -0.161
HMC 15 5.079 5.279 7.467 -0.027
HMC 30 17.167 8.067 17.680 0.515
SMC 2 16.879 8.853 16.927 0.474
SMC 5 1682.466 3.438 5.591 300.331
SMC 10 1406.382 61.875 219.151 6.135
SMC 15 2391.306 5.279 7.467 319.542
SMC 30 6602.712 8.067 17.680 372.997
Metro 2 9.122 8.853 16.927 0.016
Metro 5 5.411 3.438 5.591 0.353
Metro 10 43.808 61.875 219.151 -0.082
Metro 15 534.312 5.279 7.467 70.849
Metro 30 11754.532 8.067 17.680 664.387
DEMetro_Z 2 5.754 8.853 16.927 -0.183
DEMetro_Z 5 2591.513 3.438 5.591 462.934
DEMetro_Z 10 642.921 61.875 219.151 2.651
DEMetro_Z 15 1113.138 5.279 7.467 148.367
DEMetro_Z 30 3155.463 8.067 17.680 178.019
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.360 0.0237 0.679
HMC 5 5.671 9.99e-06 4.455
HMC 10 2.342 0.0287 1.978
HMC 15 7.792 7.71e-08 5.941
HMC 30 4.587 0.000199 20.712
SMC 2 8.617 4.77e-08 20.843
SMC 5 26.910 1.36e-16 1030.668
SMC 10 110.318 1.99e-28 310.459
SMC 15 164.049 1.93e-31 1463.582
SMC 30 251.600 5.87e-35 2933.622
Metro 2 3.772 0.00122 6.328
Metro 5 11.194 6.08e-10 21.481
Metro 10 3.019 0.00703 17.168
Metro 15 3.917 0.000926 261.586
Metro 30 6.313 4.65e-06 2313.048
DEMetro_Z 2 7.797 1.44e-08 3.755
DEMetro_Z 5 7.374 5.5e-07 804.879
DEMetro_Z 10 14.989 5.52e-12 187.741
DEMetro_Z 15 12.305 1.69e-10 1097.975
DEMetro_Z 30 20.686 1.72e-14 2476.134
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.513 0.147 0.338
Metro_vs_DEMetro_Z 1 -7.219 7.44e-07 -1.614
Metro_vs_DEMetro_Z 2 -15.478 3.17e-12 -3.461
Metro_vs_DEMetro_Z 3 -8.395 8.13e-08 -1.877
Metro_vs_DEMetro_Z 4 -0.420 0.679 -0.094
DEMetro_Z_vs_SMC 0 -6.433 3.63e-06 -1.438
DEMetro_Z_vs_SMC 1 -2.228 0.0382 -0.498
DEMetro_Z_vs_SMC 2 -9.794 7.35e-09 -2.190
DEMetro_Z_vs_SMC 3 -4.269 0.000415 -0.954
DEMetro_Z_vs_SMC 4 -3.687 0.00156 -0.824
HMC_vs_DEMetro_Z 0 -6.550 2.85e-06 -1.465
HMC_vs_DEMetro_Z 1 -7.333 5.96e-07 -1.640
HMC_vs_DEMetro_Z 2 -14.655 8.28e-12 -3.277
HMC_vs_DEMetro_Z 3 -12.234 1.87e-10 -2.736
HMC_vs_DEMetro_Z 4 -20.379 2.26e-14 -4.557
HMC_vs_Metro 0 -3.272 0.00401 -0.732
HMC_vs_Metro 1 -7.820 2.35e-07 -1.749
HMC_vs_Metro 2 -2.710 0.0139 -0.606
HMC_vs_Metro 3 -3.850 0.00108 -0.861
HMC_vs_Metro 4 -6.314 4.64e-06 -1.412
HMC_vs_SMC 0 -8.242 1.07e-07 -1.843
HMC_vs_SMC 1 -26.683 1.6e-16 -5.967
HMC_vs_SMC 2 -111.787 3.02e-28 -24.996
HMC_vs_SMC 3 -159.404 3.59e-31 -35.644
HMC_vs_SMC 4 -234.633 2.32e-34 -52.466
Metro_vs_SMC 0 -4.802 0.000124 -1.074
Metro_vs_SMC 1 -26.502 1.81e-16 -5.926
Metro_vs_SMC 2 -51.601 6.86e-22 -11.538
Metro_vs_SMC 3 -18.098 1.94e-13 -4.047
Metro_vs_SMC 4 -1.698 0.106 -0.380
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.146 0.119 0.040 0.679
HMC 5 0.215 0.100 0.026 4.455
HMC 10 0.309 0.133 0.089 1.978
HMC 15 0.246 0.099 0.025 5.941
HMC 30 0.550 0.105 0.021 20.712
SMC 2 0.946 0.119 0.040 20.843
SMC 5 26.585 0.100 0.026 1030.668
SMC 10 27.697 0.133 0.089 310.459
SMC 15 36.307 0.099 0.025 1463.582
SMC 30 63.156 0.105 0.021 2933.622
Metro 2 0.370 0.119 0.040 6.328
Metro 5 0.652 0.100 0.026 21.481
Metro 10 1.657 0.133 0.089 17.168
Metro 15 6.570 0.099 0.025 261.586
Metro 30 49.818 0.105 0.021 2313.048
DEMetro_Z 2 0.268 0.119 0.040 3.755
DEMetro_Z 5 20.783 0.100 0.026 804.879
DEMetro_Z 10 16.802 0.133 0.089 187.741
DEMetro_Z 15 27.262 0.099 0.025 1097.975
DEMetro_Z 30 53.323 0.105 0.021 2476.134
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.535 0.00116 1.307
HMC 5 3.911 0.000772 3.472
HMC 10 5.216 4.47e-05 9.527
HMC 15 7.362 3.44e-07 8.223
HMC 30 6.470 3.14e-06 17.697
SMC 2 10.538 1.99e-09 31.142
SMC 5 130.781 4.49e-32 130.268
SMC 10 118.609 1.87e-29 214.854
SMC 15 114.956 1.36e-30 122.239
SMC 30 130.787 9.63e-35 92.519
Metro 2 7.850 1.46e-07 10.023
Metro 5 8.752 4.03e-08 30.788
Metro 10 10.979 1.12e-09 76.202
Metro 15 17.767 2.56e-13 103.145
Metro 30 31.665 5.78e-18 147.763
DEMetro_Z 2 7.215 3.11e-07 5.925
DEMetro_Z 5 34.056 1.29e-18 112.991
DEMetro_Z 10 44.734 8.91e-21 234.997
DEMetro_Z 15 25.861 2.67e-16 159.974
DEMetro_Z 30 31.433 6.64e-18 146.524
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -7.899 2.02e-07 -1.766
DEMetro_Z_vs_SMC 1 -5.837 1.27e-05 -1.305
DEMetro_Z_vs_SMC 2 3.397 0.00302 0.760
DEMetro_Z_vs_SMC 3 5.965 9.68e-06 1.334
DEMetro_Z_vs_SMC 4 11.630 4.39e-10 2.601
HMC_vs_Metro 0 -6.428 3.66e-06 -1.437
HMC_vs_Metro 1 -7.997 1.69e-07 -1.788
HMC_vs_Metro 2 -8.963 2.98e-08 -2.004
HMC_vs_Metro 3 -15.844 2.09e-12 -3.543
HMC_vs_Metro 4 -25.127 4.85e-16 -5.619
Metro_vs_DEMetro_Z 0 2.847 0.0103 0.637
Metro_vs_DEMetro_Z 1 -20.869 1.47e-14 -4.666
Metro_vs_DEMetro_Z 2 -17.554 3.36e-13 -3.925
Metro_vs_DEMetro_Z 3 -6.256 5.23e-06 -1.399
Metro_vs_DEMetro_Z 4 0.201 0.843 0.045
HMC_vs_SMC 0 -9.956 5.65e-09 -2.226
HMC_vs_SMC 1 -115.709 1.57e-28 -25.873
HMC_vs_SMC 2 -84.177 6.54e-26 -18.822
HMC_vs_SMC 3 -86.916 3.57e-26 -19.435
HMC_vs_SMC 4 -24.891 5.77e-16 -5.566
Metro_vs_SMC 0 -6.450 3.5e-06 -1.442
Metro_vs_SMC 1 -28.732 4.04e-17 -6.425
Metro_vs_SMC 2 -19.706 4.17e-14 -4.406
Metro_vs_SMC 3 -3.180 0.00493 -0.711
Metro_vs_SMC 4 11.767 3.61e-10 2.631
HMC_vs_DEMetro_Z 0 -5.380 3.42e-05 -1.203
HMC_vs_DEMetro_Z 1 -34.187 1.58e-18 -7.644
HMC_vs_DEMetro_Z 2 -40.178 7.64e-20 -8.984
HMC_vs_DEMetro_Z 3 -25.121 4.87e-16 -5.617
HMC_vs_DEMetro_Z 4 -21.441 8.96e-15 -4.794
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.021 0.014 0.005 1.307
HMC 5 0.031 0.016 0.005 3.472
HMC 10 0.041 0.015 0.003 9.527
HMC 15 0.050 0.015 0.004 8.223
HMC 30 0.095 0.015 0.005 17.697
SMC 2 0.175 0.014 0.005 31.142
SMC 5 0.605 0.016 0.005 130.268
SMC 10 0.600 0.015 0.003 214.854
SMC 15 0.539 0.015 0.004 122.239
SMC 30 0.433 0.015 0.005 92.519
Metro 2 0.066 0.014 0.005 10.023
Metro 5 0.155 0.016 0.005 30.788
Metro 10 0.222 0.015 0.003 76.202
Metro 15 0.457 0.015 0.004 103.145
Metro 30 0.682 0.015 0.005 147.763
DEMetro_Z 2 0.045 0.014 0.005 5.925
DEMetro_Z 5 0.527 0.016 0.005 112.991
DEMetro_Z 10 0.655 0.015 0.003 234.997
DEMetro_Z 15 0.701 0.015 0.004 159.974
DEMetro_Z 30 0.677 0.015 0.005 146.524
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.540 0.133 0.592
HMC 5 1.860 0.0734 0.920
HMC 10 0.532 0.599 0.141
HMC 15 2.560 0.0187 3.749
HMC 30 3.827 0.00109 6.874
SMC 2 1.376 0.178 0.552
SMC 5 4.885 0.000102 40.365
SMC 10 9.906 4.57e-09 18.075
SMC 15 7.633 3.26e-07 38.753
SMC 30 27.408 9.35e-17 230.483
Metro 2 3.932 0.000752 3.726
Metro 5 3.618 0.00182 13.766
Metro 10 5.642 1.58e-05 7.531
Metro 15 4.794 0.000126 56.462
Metro 30 5.951 9.97e-06 633.994
DEMetro_Z 2 3.099 0.0043 1.480
DEMetro_Z 5 3.669 0.00163 173.897
DEMetro_Z 10 5.044 7.19e-05 47.477
DEMetro_Z 15 5.699 1.71e-05 425.392
DEMetro_Z 30 6.948 1.27e-06 1499.400
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.866 0.0775 -0.417
HMC_vs_DEMetro_Z 1 -3.638 0.00175 -0.814
HMC_vs_DEMetro_Z 2 -5.004 7.89e-05 -1.119
HMC_vs_DEMetro_Z 3 -5.642 1.93e-05 -1.262
HMC_vs_DEMetro_Z 4 -6.915 1.36e-06 -1.546
Metro_vs_SMC 0 3.352 0.00335 0.750
Metro_vs_SMC 1 -2.591 0.0179 -0.579
Metro_vs_SMC 2 -5.245 4.61e-05 -1.173
Metro_vs_SMC 3 1.292 0.212 0.289
Metro_vs_SMC 4 3.693 0.00155 0.826
Metro_vs_DEMetro_Z 0 1.955 0.0655 0.437
Metro_vs_DEMetro_Z 1 -3.350 0.00337 -0.749
Metro_vs_DEMetro_Z 2 -4.194 0.000492 -0.938
Metro_vs_DEMetro_Z 3 -5.002 7.91e-05 -1.119
Metro_vs_DEMetro_Z 4 -3.676 0.00161 -0.822
HMC_vs_Metro 0 -3.806 0.00119 -0.851
HMC_vs_Metro 1 -3.407 0.00296 -0.762
HMC_vs_Metro 2 -5.897 1.12e-05 -1.319
HMC_vs_Metro 3 -4.395 0.000311 -0.983
HMC_vs_Metro 4 -5.876 1.17e-05 -1.314
HMC_vs_SMC 0 0.081 0.936 0.018
HMC_vs_SMC 1 -4.803 0.000124 -1.074
HMC_vs_SMC 2 -10.068 4.72e-09 -2.251
HMC_vs_SMC 3 -7.013 1.12e-06 -1.568
HMC_vs_SMC 4 -26.334 2.04e-16 -5.889
DEMetro_Z_vs_SMC 0 1.457 0.161 0.326
DEMetro_Z_vs_SMC 1 2.699 0.0142 0.603
DEMetro_Z_vs_SMC 2 3.152 0.00525 0.705
DEMetro_Z_vs_SMC 3 5.198 5.12e-05 1.162
DEMetro_Z_vs_SMC 4 5.971 9.54e-06 1.335
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.096 0.067 0.049 0.592
HMC 5 0.084 0.052 0.035 0.920
HMC 10 0.097 0.082 0.109 0.141
HMC 15 0.200 0.056 0.038 3.749
HMC 30 0.322 0.062 0.038 6.874
SMC 2 0.094 0.067 0.049 0.552
SMC 5 1.448 0.052 0.035 40.365
SMC 10 2.060 0.082 0.109 18.075
SMC 15 1.544 0.056 0.038 38.753
SMC 30 8.778 0.062 0.038 230.483
Metro 2 0.249 0.067 0.049 3.726
Metro 5 0.528 0.052 0.035 13.766
Metro 10 0.906 0.082 0.109 7.531
Metro 15 2.224 0.056 0.038 56.462
Metro 30 24.038 0.062 0.038 633.994
DEMetro_Z 2 0.139 0.067 0.049 1.480
DEMetro_Z 5 6.066 0.052 0.035 173.897
DEMetro_Z 10 5.277 0.082 0.109 47.477
DEMetro_Z 15 16.396 0.056 0.038 425.392
DEMetro_Z 30 56.766 0.062 0.038 1499.400
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.972 0.341 -0.230
HMC 5 1.289 0.205 0.425
HMC 10 -1.108 0.282 -0.248
HMC 15 0.803 0.429 0.410
HMC 30 0.620 0.54 0.318
SMC 2 -0.003 0.998 -0.001
SMC 5 18.742 1.02e-13 241.697
SMC 10 21.462 1.71e-20 5.654
SMC 15 83.795 5.22e-26 326.561
SMC 30 72.483 9.27e-25 358.053
Metro 2 -0.566 0.576 -0.135
Metro 5 1.199 0.245 2.086
Metro 10 -1.134 0.271 -0.254
Metro 15 2.175 0.0424 10.234
Metro 30 2.333 0.0308 87.834
DEMetro_Z 2 -0.750 0.461 -0.180
DEMetro_Z 5 1.732 0.0994 270.100
DEMetro_Z 10 2.149 0.038 0.664
DEMetro_Z 15 3.809 0.00118 52.221
DEMetro_Z 30 8.828 3.64e-08 43.461
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -2.113 0.048 -0.473
HMC_vs_SMC 1 -18.770 1.01e-13 -4.197
HMC_vs_SMC 2 -42.130 3.13e-20 -9.421
HMC_vs_SMC 3 -82.310 1e-25 -18.405
HMC_vs_SMC 4 -71.151 1.58e-24 -15.910
Metro_vs_DEMetro_Z 0 0.866 0.398 0.194
Metro_vs_DEMetro_Z 1 -1.719 0.102 -0.384
Metro_vs_DEMetro_Z 2 -4.292 0.000394 -0.960
Metro_vs_DEMetro_Z 3 -2.937 0.00847 -0.657
Metro_vs_DEMetro_Z 4 1.153 0.263 0.258
HMC_vs_Metro 0 -2.115 0.0478 -0.473
HMC_vs_Metro 1 -0.964 0.347 -0.216
HMC_vs_Metro 2 0.624 0.54 0.140
HMC_vs_Metro 3 -2.080 0.0513 -0.465
HMC_vs_Metro 4 -2.324 0.0314 -0.520
HMC_vs_DEMetro_Z 0 -2.579 0.0184 -0.577
HMC_vs_DEMetro_Z 1 -1.730 0.0999 -0.387
HMC_vs_DEMetro_Z 2 -4.236 0.000447 -0.947
HMC_vs_DEMetro_Z 3 -3.749 0.00136 -0.838
HMC_vs_DEMetro_Z 4 -8.605 5.58e-08 -1.924
Metro_vs_SMC 0 -1.432 0.168 -0.320
Metro_vs_SMC 1 -17.992 2.16e-13 -4.023
Metro_vs_SMC 2 -42.065 3.22e-20 -9.406
Metro_vs_SMC 3 -58.153 7.18e-23 -13.003
Metro_vs_SMC 4 -6.900 1.4e-06 -1.543
DEMetro_Z_vs_SMC 0 -1.588 0.129 -0.355
DEMetro_Z_vs_SMC 1 0.181 0.858 0.040
DEMetro_Z_vs_SMC 2 -24.856 5.92e-16 -5.558
DEMetro_Z_vs_SMC 3 -20.600 1.86e-14 -4.606
DEMetro_Z_vs_SMC 4 -45.547 7.22e-21 -10.185
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 4.965 8.853 16.927 -0.230
HMC 5 5.817 3.438 5.591 0.425
HMC 10 7.536 61.875 219.151 -0.248
HMC 15 8.339 5.279 7.467 0.410
HMC 30 13.690 8.067 17.680 0.318
SMC 2 8.842 8.853 16.927 -0.001
SMC 5 1354.669 3.438 5.591 241.697
SMC 10 1301.003 61.875 219.151 5.654
SMC 15 2443.717 5.279 7.467 326.561
SMC 30 6338.502 8.067 17.680 358.053
Metro 2 6.576 8.853 16.927 -0.135
Metro 5 15.103 3.438 5.591 2.086
Metro 10 6.267 61.875 219.151 -0.254
Metro 15 81.698 5.279 7.467 10.234
Metro 30 1560.983 8.067 17.680 87.834
DEMetro_Z 2 5.813 8.853 16.927 -0.180
DEMetro_Z 5 1513.458 3.438 5.591 270.100
DEMetro_Z 10 207.394 61.875 219.151 0.664
DEMetro_Z 15 395.213 5.279 7.467 52.221
DEMetro_Z 30 776.459 8.067 17.680 43.461
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.985 0.00031 1.411
HMC 5 4.493 0.000211 5.205
HMC 10 3.310 0.00223 1.308
HMC 15 4.760 0.000127 9.170
HMC 30 3.435 0.00277 21.899
SMC 2 5.219 4.56e-05 11.168
SMC 5 25.102 4.93e-16 918.302
SMC 10 66.652 4.35e-24 291.968
SMC 15 88.023 2.76e-26 1478.330
SMC 30 139.415 4.5e-30 2855.314
Metro 2 6.378 2.64e-06 6.668
Metro 5 3.175 0.00497 26.685
Metro 10 7.353 3.83e-07 9.066
Metro 15 5.261 4.45e-05 111.172
Metro 30 5.316 3.94e-05 1135.589
DEMetro_Z 2 6.709 2.66e-07 3.306
DEMetro_Z 5 3.489 0.00246 365.123
DEMetro_Z 10 6.799 1.71e-06 87.526
DEMetro_Z 15 8.312 9.46e-08 731.363
DEMetro_Z 30 8.063 1.49e-07 2373.284
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 2.763 0.0124 0.618
Metro_vs_DEMetro_Z 1 -3.186 0.00487 -0.712
Metro_vs_DEMetro_Z 2 -6.019 8.62e-06 -1.346
Metro_vs_DEMetro_Z 3 -7.154 8.45e-07 -1.600
Metro_vs_DEMetro_Z 4 -3.250 0.00421 -0.727
DEMetro_Z_vs_SMC 0 -3.411 0.00293 -0.763
DEMetro_Z_vs_SMC 1 -4.970 8.51e-05 -1.111
DEMetro_Z_vs_SMC 2 -16.465 1.06e-12 -3.682
DEMetro_Z_vs_SMC 3 -8.276 1.01e-07 -1.851
DEMetro_Z_vs_SMC 4 -1.679 0.109 -0.375
HMC_vs_DEMetro_Z 0 -3.623 0.00181 -0.810
HMC_vs_DEMetro_Z 1 -3.439 0.00275 -0.769
HMC_vs_DEMetro_Z 2 -6.653 2.31e-06 -1.488
HMC_vs_DEMetro_Z 3 -8.133 1.31e-07 -1.819
HMC_vs_DEMetro_Z 4 -7.981 1.73e-07 -1.785
HMC_vs_Metro 0 -5.094 6.45e-05 -1.139
HMC_vs_Metro 1 -2.602 0.0175 -0.582
HMC_vs_Metro 2 -7.137 8.75e-07 -1.596
HMC_vs_Metro 3 -4.727 0.000147 -1.057
HMC_vs_Metro 4 -5.242 4.64e-05 -1.172
HMC_vs_SMC 0 -4.714 0.000151 -1.054
HMC_vs_SMC 1 -24.780 6.27e-16 -5.541
HMC_vs_SMC 2 -66.351 5.93e-24 -14.836
HMC_vs_SMC 3 -88.602 2.48e-26 -19.812
HMC_vs_SMC 4 -138.581 5.11e-30 -30.988
Metro_vs_SMC 0 -2.169 0.043 -0.485
Metro_vs_SMC 1 -22.830 2.84e-15 -5.105
Metro_vs_SMC 2 -63.848 1.23e-23 -14.277
Metro_vs_SMC 3 -50.862 9.01e-22 -11.373
Metro_vs_SMC 4 -7.776 2.55e-07 -1.739
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.175 0.119 0.040 1.411
HMC 5 0.234 0.100 0.026 5.205
HMC 10 0.249 0.133 0.089 1.308
HMC 15 0.326 0.099 0.025 9.170
HMC 30 0.575 0.105 0.021 21.899
SMC 2 0.562 0.119 0.040 11.168
SMC 5 23.698 0.100 0.026 918.302
SMC 10 26.056 0.133 0.089 291.968
SMC 15 36.672 0.099 0.025 1478.330
SMC 30 61.473 0.105 0.021 2855.314
Metro 2 0.383 0.119 0.040 6.668
Metro 5 0.786 0.100 0.026 26.685
Metro 10 0.938 0.133 0.089 9.066
Metro 15 2.849 0.099 0.025 111.172
Metro 30 24.511 0.105 0.021 1135.589
DEMetro_Z 2 0.250 0.119 0.040 3.306
DEMetro_Z 5 9.483 0.100 0.026 365.123
DEMetro_Z 10 7.904 0.133 0.089 87.526
DEMetro_Z 15 18.192 0.099 0.025 731.363
DEMetro_Z 30 51.113 0.105 0.021 2373.284
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.094 0.000347 2.163
HMC 5 5.414 1.94e-05 4.452
HMC 10 4.574 0.000199 10.703
HMC 15 7.127 6.04e-07 8.699
HMC 30 3.591 0.00195 25.852
SMC 2 7.189 7.4e-07 21.942
SMC 5 90.253 1.71e-27 131.698
SMC 10 115.216 3.74e-29 217.125
SMC 15 83.060 1.07e-26 126.456
SMC 30 167.108 4.85e-41 92.885
Metro 2 8.933 1.86e-08 11.308
Metro 5 7.480 4.34e-07 32.508
Metro 10 6.942 1.28e-06 82.426
Metro 15 10.792 1.5e-09 105.305
Metro 30 26.482 1.73e-16 174.479
DEMetro_Z 2 10.540 1.12e-11 4.710
DEMetro_Z 5 9.169 2.07e-08 84.759
DEMetro_Z 10 20.983 1.3e-14 193.005
DEMetro_Z 15 19.636 4.34e-14 180.147
DEMetro_Z 30 20.500 1.98e-14 183.916
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -5.709 1.67e-05 -1.277
DEMetro_Z_vs_SMC 1 -4.995 8.04e-05 -1.117
DEMetro_Z_vs_SMC 2 -2.459 0.0237 -0.550
DEMetro_Z_vs_SMC 3 5.872 1.18e-05 1.313
DEMetro_Z_vs_SMC 4 10.227 3.66e-09 2.287
HMC_vs_Metro 0 -7.490 4.4e-07 -1.675
HMC_vs_Metro 1 -6.972 1.21e-06 -1.559
HMC_vs_Metro 2 -5.969 9.6e-06 -1.335
HMC_vs_Metro 3 -9.648 9.34e-09 -2.157
HMC_vs_Metro 4 -15.394 3.48e-12 -3.442
Metro_vs_DEMetro_Z 0 4.814 0.000121 1.076
Metro_vs_DEMetro_Z 1 -4.944 9.01e-05 -1.106
Metro_vs_DEMetro_Z 2 -6.292 4.86e-06 -1.407
Metro_vs_DEMetro_Z 3 -4.684 0.000162 -1.047
Metro_vs_DEMetro_Z 4 -0.859 0.401 -0.192
HMC_vs_SMC 0 -6.897 1.41e-06 -1.542
HMC_vs_SMC 1 -71.040 1.63e-24 -15.885
HMC_vs_SMC 2 -73.092 9.5e-25 -16.344
HMC_vs_SMC 3 -78.074 2.72e-25 -17.458
HMC_vs_SMC 4 -9.219 1.92e-08 -2.061
Metro_vs_SMC 0 -3.590 0.00195 -0.803
Metro_vs_SMC 1 -19.410 5.48e-14 -4.340
Metro_vs_SMC 2 -11.667 4.16e-10 -2.609
Metro_vs_SMC 3 -2.039 0.0556 -0.456
Metro_vs_SMC 4 12.684 1.01e-10 2.836
HMC_vs_DEMetro_Z 0 -3.958 0.000843 -0.885
HMC_vs_DEMetro_Z 1 -8.471 7.1e-08 -1.894
HMC_vs_DEMetro_Z 2 -18.944 8.52e-14 -4.236
HMC_vs_DEMetro_Z 3 -19.054 7.67e-14 -4.261
HMC_vs_DEMetro_Z 4 -14.320 1.24e-11 -3.202
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.025 0.014 0.005 2.163
HMC 5 0.036 0.016 0.005 4.452
HMC 10 0.044 0.015 0.003 10.703
HMC 15 0.052 0.015 0.004 8.699
HMC 30 0.131 0.015 0.005 25.852
SMC 2 0.127 0.014 0.005 21.942
SMC 5 0.611 0.016 0.005 131.698
SMC 10 0.606 0.015 0.003 217.125
SMC 15 0.557 0.015 0.004 126.456
SMC 30 0.434 0.015 0.005 92.885
Metro 2 0.073 0.014 0.005 11.308
Metro 5 0.163 0.016 0.005 32.508
Metro 10 0.239 0.015 0.003 82.426
Metro 15 0.467 0.015 0.004 105.305
Metro 30 0.803 0.015 0.005 174.479
DEMetro_Z 2 0.039 0.014 0.005 4.710
DEMetro_Z 5 0.399 0.016 0.005 84.759
DEMetro_Z 10 0.541 0.015 0.003 193.005
DEMetro_Z 15 0.788 0.015 0.004 180.147
DEMetro_Z 30 0.846 0.015 0.005 183.916
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Multimodal_Distance

▼

Varying_only_Mode_distance (Mixture, mm, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.569 0.000161 4.248
HMC 8 5.056 6.96e-05 31.189
HMC 10 4.929 9.21e-05 23.032
HMC 12 3.783 0.00125 20.146
HMC 15 4.033 0.000707 24.978
HMC 18 6.007 8.72e-06 32.634
SMC 5 -1.149 0.258 -0.330
SMC 8 1.050 0.301 0.425
SMC 10 1.455 0.154 0.442
SMC 12 0.802 0.428 0.250
SMC 15 0.187 0.853 0.061
SMC 18 -0.998 0.325 -0.286
Metro 5 3.262 0.003 1.717
Metro 8 7.017 1.02e-06 18.327
Metro 10 6.223 5.47e-06 26.832
Metro 12 4.166 0.000521 22.274
Metro 15 4.067 0.000654 25.160
Metro 18 6.086 7.38e-06 34.401
DEMetro_Z 5 2.780 0.00898 1.149
DEMetro_Z 8 6.431 3.46e-06 20.096
DEMetro_Z 10 4.829 0.000113 14.129
DEMetro_Z 12 4.531 0.000223 13.915
DEMetro_Z 15 4.674 0.000164 24.305
DEMetro_Z 18 6.675 2.15e-06 30.800
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 3.248 0.00423 0.726
HMC_vs_DEMetro_Z 1 1.328 0.2 0.297
HMC_vs_DEMetro_Z 2 1.711 0.103 0.383
HMC_vs_DEMetro_Z 3 1.119 0.277 0.250
HMC_vs_DEMetro_Z 4 0.111 0.913 0.025
HMC_vs_DEMetro_Z 5 0.329 0.746 0.074
Metro_vs_SMC 0 3.818 0.00116 0.854
Metro_vs_SMC 1 6.873 1.48e-06 1.537
Metro_vs_SMC 2 6.131 6.81e-06 1.371
Metro_vs_SMC 3 4.152 0.000541 0.928
Metro_vs_SMC 4 4.064 0.000662 0.909
Metro_vs_SMC 5 6.160 6.4e-06 1.378
Metro_vs_DEMetro_Z 0 1.012 0.324 0.226
Metro_vs_DEMetro_Z 1 -0.445 0.662 -0.099
Metro_vs_DEMetro_Z 2 2.611 0.0172 0.584
Metro_vs_DEMetro_Z 3 1.609 0.124 0.360
Metro_vs_DEMetro_Z 4 0.150 0.882 0.034
Metro_vs_DEMetro_Z 5 0.615 0.546 0.138
HMC_vs_Metro 0 2.346 0.03 0.525
HMC_vs_Metro 1 1.892 0.0738 0.423
HMC_vs_Metro 2 -0.567 0.577 -0.127
HMC_vs_Metro 3 -0.680 0.504 -0.152
HMC_vs_Metro 4 -0.056 0.956 -0.012
HMC_vs_Metro 5 -0.598 0.557 -0.134
HMC_vs_SMC 0 5.320 3.91e-05 1.190
HMC_vs_SMC 1 4.972 8.47e-05 1.112
HMC_vs_SMC 2 4.844 0.000113 1.083
HMC_vs_SMC 3 3.758 0.00133 0.840
HMC_vs_SMC 4 4.022 0.000729 0.899
HMC_vs_SMC 5 6.091 7.41e-06 1.362
DEMetro_Z_vs_SMC 0 3.388 0.00309 0.758
DEMetro_Z_vs_SMC 1 6.233 5.49e-06 1.394
DEMetro_Z_vs_SMC 2 4.748 0.00014 1.062
DEMetro_Z_vs_SMC 3 4.505 0.000242 1.007
DEMetro_Z_vs_SMC 4 4.623 0.000185 1.034
DEMetro_Z_vs_SMC 5 6.723 2e-06 1.503
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.180 0.045 0.032 4.248
HMC 8 0.978 0.051 0.030 31.189
HMC 10 1.173 0.054 0.049 23.032
HMC 12 1.505 0.089 0.070 20.146
HMC 15 1.510 0.086 0.057 24.978
HMC 18 3.204 0.128 0.094 32.634
SMC 5 0.035 0.045 0.032 -0.330
SMC 8 0.064 0.051 0.030 0.425
SMC 10 0.076 0.054 0.049 0.442
SMC 12 0.107 0.089 0.070 0.250
SMC 15 0.089 0.086 0.057 0.061
SMC 18 0.101 0.128 0.094 -0.286
Metro 5 0.100 0.045 0.032 1.717
Metro 8 0.596 0.051 0.030 18.327
Metro 10 1.358 0.054 0.049 26.832
Metro 12 1.654 0.089 0.070 22.274
Metro 15 1.521 0.086 0.057 25.160
Metro 18 3.370 0.128 0.094 34.401
DEMetro_Z 5 0.082 0.045 0.032 1.149
DEMetro_Z 8 0.649 0.051 0.030 20.096
DEMetro_Z 10 0.741 0.054 0.049 14.129
DEMetro_Z 12 1.067 0.089 0.070 13.915
DEMetro_Z 15 1.472 0.086 0.057 24.305
DEMetro_Z 18 3.031 0.128 0.094 30.800
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.882 0.00688 1.158
HMC 8 2.889 0.0094 29.112
HMC 10 3.667 0.00164 40.058
HMC 12 3.128 0.00554 64.473
HMC 15 3.110 0.00577 60.472
HMC 18 4.359 0.000338 150.045
SMC 5 0.428 0.671 0.116
SMC 8 1.056 0.298 0.295
SMC 10 0.397 0.693 0.131
SMC 12 -0.987 0.33 -0.293
SMC 15 -1.057 0.297 -0.310
SMC 18 0.821 0.418 0.320
Metro 5 3.036 0.00468 1.245
Metro 8 4.255 0.000404 7.851
Metro 10 3.956 0.000845 48.051
Metro 12 3.463 0.0026 69.948
Metro 15 3.070 0.00631 59.656
Metro 18 4.519 0.000235 164.941
DEMetro_Z 5 3.516 0.00158 1.861
DEMetro_Z 8 4.432 0.000275 10.232
DEMetro_Z 10 2.583 0.0182 15.217
DEMetro_Z 12 2.137 0.0458 25.513
DEMetro_Z 15 2.521 0.0208 48.308
DEMetro_Z 18 4.314 0.000374 125.419
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.165 0.0051 0.708
HMC_vs_SMC 1 2.857 0.0101 0.639
HMC_vs_SMC 2 3.656 0.00168 0.818
HMC_vs_SMC 3 3.151 0.00527 0.704
HMC_vs_SMC 4 3.137 0.00543 0.701
HMC_vs_SMC 5 4.342 0.000351 0.971
Metro_vs_DEMetro_Z 0 -0.977 0.341 -0.218
Metro_vs_DEMetro_Z 1 -0.780 0.445 -0.174
Metro_vs_DEMetro_Z 2 2.940 0.0084 0.658
Metro_vs_DEMetro_Z 3 2.532 0.0203 0.566
Metro_vs_DEMetro_Z 4 0.538 0.597 0.120
Metro_vs_DEMetro_Z 5 0.919 0.37 0.205
HMC_vs_Metro 0 -0.165 0.87 -0.037
HMC_vs_Metro 1 2.038 0.0558 0.456
HMC_vs_Metro 2 -0.458 0.652 -0.102
HMC_vs_Metro 3 -0.319 0.753 -0.071
HMC_vs_Metro 4 0.129 0.899 0.029
HMC_vs_Metro 5 -0.886 0.387 -0.198
HMC_vs_DEMetro_Z 0 -1.183 0.251 -0.264
HMC_vs_DEMetro_Z 1 1.711 0.103 0.382
HMC_vs_DEMetro_Z 2 1.993 0.0609 0.446
HMC_vs_DEMetro_Z 3 1.992 0.0609 0.445
HMC_vs_DEMetro_Z 4 0.558 0.583 0.125
HMC_vs_DEMetro_Z 5 0.617 0.544 0.138
Metro_vs_SMC 0 2.792 0.0116 0.624
Metro_vs_SMC 1 4.243 0.00044 0.949
Metro_vs_SMC 2 3.915 0.000931 0.875
Metro_vs_SMC 3 3.481 0.0025 0.778
Metro_vs_SMC 4 3.098 0.00592 0.693
Metro_vs_SMC 5 4.504 0.000243 1.007
DEMetro_Z_vs_SMC 0 3.460 0.00262 0.774
DEMetro_Z_vs_SMC 1 4.271 0.000413 0.955
DEMetro_Z_vs_SMC 2 2.571 0.0187 0.575
DEMetro_Z_vs_SMC 3 2.151 0.0446 0.481
DEMetro_Z_vs_SMC 4 2.542 0.0199 0.568
DEMetro_Z_vs_SMC 5 4.296 0.00039 0.961
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.106 0.048 0.050 1.158
HMC 8 2.207 0.081 0.073 29.112
HMC 10 3.366 0.119 0.081 40.058
HMC 12 7.052 0.161 0.107 64.473
HMC 15 6.627 0.204 0.106 60.472
HMC 18 21.541 0.197 0.142 150.045
SMC 5 0.054 0.048 0.050 0.116
SMC 8 0.103 0.081 0.073 0.295
SMC 10 0.129 0.119 0.081 0.131
SMC 12 0.130 0.161 0.107 -0.293
SMC 15 0.172 0.204 0.106 -0.310
SMC 18 0.242 0.197 0.142 0.320
Metro 5 0.110 0.048 0.050 1.245
Metro 8 0.654 0.081 0.073 7.851
Metro 10 4.014 0.119 0.081 48.051
Metro 12 7.638 0.161 0.107 69.948
Metro 15 6.540 0.204 0.106 59.656
Metro 18 23.660 0.197 0.142 164.941
DEMetro_Z 5 0.141 0.048 0.050 1.861
DEMetro_Z 8 0.828 0.081 0.073 10.232
DEMetro_Z 10 1.352 0.119 0.081 15.217
DEMetro_Z 12 2.888 0.161 0.107 25.513
DEMetro_Z 15 5.335 0.204 0.106 48.308
DEMetro_Z 18 18.038 0.197 0.142 125.419
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.519 0.000191 4.722
HMC 8 5.200 5.07e-05 40.217
HMC 10 4.681 0.000162 27.854
HMC 12 3.736 0.00139 21.268
HMC 15 4.032 0.000709 28.597
HMC 18 6.024 8.42e-06 34.348
SMC 5 -1.412 0.167 -0.404
SMC 8 1.299 0.204 0.595
SMC 10 1.468 0.15 0.476
SMC 12 0.656 0.515 0.208
SMC 15 0.552 0.584 0.186
SMC 18 -0.894 0.378 -0.252
Metro 5 3.903 0.000592 2.139
Metro 8 7.035 1.02e-06 23.748
Metro 10 6.459 3.37e-06 32.217
Metro 12 4.174 0.000513 24.632
Metro 15 3.915 0.000928 30.246
Metro 18 6.065 7.73e-06 35.557
DEMetro_Z 5 5.578 2.94e-06 2.144
DEMetro_Z 8 6.588 2.55e-06 25.929
DEMetro_Z 10 5.006 7.65e-05 17.063
DEMetro_Z 12 4.368 0.000326 15.158
DEMetro_Z 15 4.697 0.000156 29.210
DEMetro_Z 18 6.703 2.04e-06 33.047
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.009 0.993 -0.002
Metro_vs_DEMetro_Z 1 -0.438 0.666 -0.098
Metro_vs_DEMetro_Z 2 2.718 0.0136 0.608
Metro_vs_DEMetro_Z 3 1.687 0.108 0.377
Metro_vs_DEMetro_Z 4 0.151 0.881 0.034
Metro_vs_DEMetro_Z 5 0.410 0.686 0.092
DEMetro_Z_vs_SMC 0 6.405 3.84e-06 1.432
DEMetro_Z_vs_SMC 1 6.343 4.37e-06 1.418
DEMetro_Z_vs_SMC 2 4.930 9.31e-05 1.102
DEMetro_Z_vs_SMC 3 4.350 0.000345 0.973
DEMetro_Z_vs_SMC 4 4.644 0.000177 1.038
DEMetro_Z_vs_SMC 5 6.753 1.88e-06 1.510
HMC_vs_DEMetro_Z 0 2.361 0.0291 0.528
HMC_vs_DEMetro_Z 1 1.364 0.188 0.305
HMC_vs_DEMetro_Z 2 1.660 0.113 0.371
HMC_vs_DEMetro_Z 3 1.046 0.309 0.234
HMC_vs_DEMetro_Z 4 -0.086 0.932 -0.019
HMC_vs_DEMetro_Z 5 0.224 0.825 0.050
HMC_vs_Metro 0 2.235 0.0376 0.500
HMC_vs_Metro 1 1.890 0.0741 0.423
HMC_vs_Metro 2 -0.520 0.609 -0.116
HMC_vs_Metro 3 -0.900 0.38 -0.201
HMC_vs_Metro 4 -0.455 0.654 -0.102
HMC_vs_Metro 5 -0.361 0.722 -0.081
HMC_vs_SMC 0 5.391 3.35e-05 1.205
HMC_vs_SMC 1 5.088 6.54e-05 1.138
HMC_vs_SMC 2 4.605 0.000193 1.030
HMC_vs_SMC 3 3.718 0.00146 0.831
HMC_vs_SMC 4 4.016 0.000738 0.898
HMC_vs_SMC 5 6.100 7.26e-06 1.364
Metro_vs_SMC 0 4.811 0.000121 1.076
Metro_vs_SMC 1 6.808 1.69e-06 1.522
Metro_vs_SMC 2 6.389 3.97e-06 1.429
Metro_vs_SMC 3 4.171 0.000519 0.933
Metro_vs_SMC 4 3.908 0.000945 0.874
Metro_vs_SMC 5 6.130 6.82e-06 1.371
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.169 0.057 0.024 4.722
HMC 8 0.870 0.060 0.020 40.217
HMC 10 1.068 0.068 0.036 27.854
HMC 12 1.330 0.097 0.058 21.268
HMC 15 1.355 0.090 0.044 28.597
HMC 18 2.890 0.132 0.080 34.348
SMC 5 0.047 0.057 0.024 -0.404
SMC 8 0.072 0.060 0.020 0.595
SMC 10 0.085 0.068 0.036 0.476
SMC 12 0.109 0.097 0.058 0.208
SMC 15 0.098 0.090 0.044 0.186
SMC 18 0.112 0.132 0.080 -0.252
Metro 5 0.107 0.057 0.024 2.139
Metro 8 0.538 0.060 0.020 23.748
Metro 10 1.224 0.068 0.036 32.217
Metro 12 1.525 0.097 0.058 24.632
Metro 15 1.428 0.090 0.044 30.246
Metro 18 2.987 0.132 0.080 35.557
DEMetro_Z 5 0.108 0.057 0.024 2.144
DEMetro_Z 8 0.582 0.060 0.020 25.929
DEMetro_Z 10 0.680 0.068 0.036 17.063
DEMetro_Z 12 0.975 0.097 0.058 15.158
DEMetro_Z 15 1.382 0.090 0.044 29.210
DEMetro_Z 18 2.785 0.132 0.080 33.047
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.713 0.000126 5.484
HMC 8 4.997 7.96e-05 35.557
HMC 10 4.937 9.08e-05 27.802
HMC 12 3.839 0.0011 21.237
HMC 15 4.083 0.000632 29.920
HMC 18 6.252 5.21e-06 38.047
SMC 5 -1.012 0.318 -0.302
SMC 8 0.968 0.34 0.398
SMC 10 1.566 0.126 0.499
SMC 12 0.747 0.46 0.234
SMC 15 0.349 0.729 0.115
SMC 18 -0.922 0.363 -0.273
Metro 5 4.004 0.00051 2.518
Metro 8 6.686 2.04e-06 20.476
Metro 10 6.273 4.97e-06 31.862
Metro 12 4.265 0.000415 23.307
Metro 15 4.112 0.000592 29.673
Metro 18 6.322 4.51e-06 40.626
DEMetro_Z 5 4.691 5.34e-05 2.081
DEMetro_Z 8 6.437 3.47e-06 23.426
DEMetro_Z 10 4.921 9.27e-05 17.216
DEMetro_Z 12 4.730 0.000142 14.798
DEMetro_Z 15 5.009 7.73e-05 29.145
DEMetro_Z 18 6.936 1.28e-06 36.630
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.814 0.000121 1.076
DEMetro_Z_vs_SMC 1 6.270 5.09e-06 1.402
DEMetro_Z_vs_SMC 2 4.833 0.000115 1.081
DEMetro_Z_vs_SMC 3 4.727 0.000147 1.057
DEMetro_Z_vs_SMC 4 4.951 8.87e-05 1.107
DEMetro_Z_vs_SMC 5 6.975 1.21e-06 1.560
HMC_vs_Metro 0 2.249 0.0366 0.503
HMC_vs_Metro 1 1.925 0.0693 0.431
HMC_vs_Metro 2 -0.505 0.62 -0.113
HMC_vs_Metro 3 -0.656 0.519 -0.147
HMC_vs_Metro 4 0.064 0.95 0.014
HMC_vs_Metro 5 -0.727 0.476 -0.163
Metro_vs_DEMetro_Z 0 0.726 0.477 0.162
Metro_vs_DEMetro_Z 1 -0.632 0.535 -0.141
Metro_vs_DEMetro_Z 2 2.561 0.0191 0.573
Metro_vs_DEMetro_Z 3 1.566 0.134 0.350
Metro_vs_DEMetro_Z 4 0.081 0.937 0.018
Metro_vs_DEMetro_Z 5 0.604 0.553 0.135
HMC_vs_SMC 0 5.345 3.7e-05 1.195
HMC_vs_SMC 1 4.933 9.24e-05 1.103
HMC_vs_SMC 2 4.875 0.000105 1.090
HMC_vs_SMC 3 3.826 0.00114 0.856
HMC_vs_SMC 4 4.074 0.000647 0.911
HMC_vs_SMC 5 6.318 4.6e-06 1.413
Metro_vs_SMC 0 4.421 0.000293 0.989
Metro_vs_SMC 1 6.577 2.7e-06 1.471
Metro_vs_SMC 2 6.198 5.91e-06 1.386
Metro_vs_SMC 3 4.259 0.000424 0.952
Metro_vs_SMC 4 4.104 0.000605 0.918
Metro_vs_SMC 5 6.390 3.96e-06 1.429
HMC_vs_DEMetro_Z 0 2.746 0.0128 0.614
HMC_vs_DEMetro_Z 1 1.256 0.224 0.281
HMC_vs_DEMetro_Z 2 1.698 0.106 0.380
HMC_vs_DEMetro_Z 3 1.090 0.289 0.244
HMC_vs_DEMetro_Z 4 0.110 0.914 0.025
HMC_vs_DEMetro_Z 5 0.228 0.822 0.051
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.053 0.015 0.007 5.484
HMC 8 0.212 0.012 0.006 35.557
HMC 10 0.213 0.011 0.007 27.802
HMC 12 0.229 0.014 0.010 21.237
HMC 15 0.186 0.010 0.006 29.920
HMC 18 0.317 0.012 0.008 38.047
SMC 5 0.013 0.015 0.007 -0.302
SMC 8 0.014 0.012 0.006 0.398
SMC 10 0.014 0.011 0.007 0.499
SMC 12 0.016 0.014 0.010 0.234
SMC 15 0.010 0.010 0.006 0.115
SMC 18 0.010 0.012 0.008 -0.273
Metro 5 0.032 0.015 0.007 2.518
Metro 8 0.127 0.012 0.006 20.476
Metro 10 0.243 0.011 0.007 31.862
Metro 12 0.250 0.014 0.010 23.307
Metro 15 0.185 0.010 0.006 29.673
Metro 18 0.338 0.012 0.008 40.626
DEMetro_Z 5 0.029 0.015 0.007 2.081
DEMetro_Z 8 0.144 0.012 0.006 23.426
DEMetro_Z 10 0.136 0.011 0.007 17.216
DEMetro_Z 12 0.163 0.014 0.010 14.798
DEMetro_Z 15 0.182 0.010 0.006 29.145
DEMetro_Z 18 0.305 0.012 0.008 36.630
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.179 0.000296 2.359
HMC 8 7.671 3.08e-07 60.191
HMC 10 205.835 5.26e-58 71.745
HMC 12 200.525 6.99e-58 58.922
HMC 15 220.540 5.41e-53 91.369
HMC 18 239.669 2.83e-57 66.098
SMC 5 -0.464 0.646 -0.156
SMC 8 1.193 0.24 0.416
SMC 10 0.656 0.516 0.200
SMC 12 -0.229 0.82 -0.062
SMC 15 1.250 0.22 0.496
SMC 18 -0.412 0.683 -0.118
Metro 5 3.764 0.000889 2.193
Metro 8 5.229 4.63e-05 16.633
Metro 10 5.898 1.09e-05 27.102
Metro 12 21.318 7.16e-15 55.143
Metro 15 206.644 5.07e-50 90.767
Metro 18 233.491 1.47e-58 66.074
DEMetro_Z 5 3.117 0.00431 1.644
DEMetro_Z 8 3.374 0.00313 7.758
DEMetro_Z 10 4.249 0.000433 30.353
DEMetro_Z 12 8.119 1.31e-07 44.906
DEMetro_Z 15 22.247 3.95e-15 88.233
DEMetro_Z 18 11.225 7.58e-10 56.832
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.999 0.331 0.223
HMC_vs_DEMetro_Z 1 6.847 1.56e-06 1.531
HMC_vs_DEMetro_Z 2 5.744 1.55e-05 1.284
HMC_vs_DEMetro_Z 3 2.516 0.021 0.563
HMC_vs_DEMetro_Z 4 0.791 0.439 0.177
HMC_vs_DEMetro_Z 5 1.823 0.084 0.408
Metro_vs_SMC 0 4.580 0.000205 1.024
Metro_vs_SMC 1 5.115 6.16e-05 1.144
Metro_vs_SMC 2 5.970 9.56e-06 1.335
Metro_vs_SMC 3 21.431 9.04e-15 4.792
Metro_vs_SMC 4 138.245 5.35e-30 30.913
Metro_vs_SMC 5 244.951 1.03e-34 54.773
Metro_vs_DEMetro_Z 0 0.750 0.462 0.168
Metro_vs_DEMetro_Z 1 2.012 0.0587 0.450
Metro_vs_DEMetro_Z 2 -0.340 0.738 -0.076
Metro_vs_DEMetro_Z 3 1.549 0.138 0.346
Metro_vs_DEMetro_Z 4 0.633 0.535 0.141
Metro_vs_DEMetro_Z 5 1.817 0.0851 0.406
HMC_vs_Metro 0 0.225 0.824 0.050
HMC_vs_Metro 1 5.421 3.13e-05 1.212
HMC_vs_Metro 2 9.637 9.51e-09 2.155
HMC_vs_Metro 3 1.465 0.159 0.327
HMC_vs_Metro 4 1.362 0.189 0.304
HMC_vs_Metro 5 0.484 0.634 0.108
HMC_vs_SMC 0 4.350 0.000345 0.973
HMC_vs_SMC 1 7.588 3.64e-07 1.697
HMC_vs_SMC 2 200.966 4.4e-33 44.937
HMC_vs_SMC 3 192.060 1.04e-32 42.946
HMC_vs_SMC 4 216.343 1.09e-33 48.376
HMC_vs_SMC 5 248.277 7.94e-35 55.516
DEMetro_Z_vs_SMC 0 3.021 0.00703 0.675
DEMetro_Z_vs_SMC 1 3.370 0.00322 0.754
DEMetro_Z_vs_SMC 2 4.251 0.000433 0.950
DEMetro_Z_vs_SMC 3 8.103 1.39e-07 1.812
DEMetro_Z_vs_SMC 4 22.575 3.49e-15 5.048
DEMetro_Z_vs_SMC 5 11.258 7.56e-10 2.517
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.120 0.045 0.032 2.359
HMC 8 1.840 0.051 0.030 60.191
HMC 10 3.539 0.054 0.049 71.745
HMC 12 4.229 0.089 0.070 58.922
HMC 15 5.298 0.086 0.057 91.369
HMC 18 6.358 0.128 0.094 66.098
SMC 5 0.040 0.045 0.032 -0.156
SMC 8 0.064 0.051 0.030 0.416
SMC 10 0.064 0.054 0.049 0.200
SMC 12 0.085 0.089 0.070 -0.062
SMC 15 0.114 0.086 0.057 0.496
SMC 18 0.117 0.128 0.094 -0.118
Metro 5 0.115 0.045 0.032 2.193
Metro 8 0.546 0.051 0.030 16.633
Metro 10 1.371 0.054 0.049 27.102
Metro 12 3.964 0.089 0.070 55.143
Metro 15 5.263 0.086 0.057 90.767
Metro 18 6.355 0.128 0.094 66.074
DEMetro_Z 5 0.097 0.045 0.032 1.644
DEMetro_Z 8 0.282 0.051 0.030 7.758
DEMetro_Z 10 1.529 0.054 0.049 30.353
DEMetro_Z 12 3.245 0.089 0.070 44.906
DEMetro_Z 15 5.119 0.086 0.057 88.233
DEMetro_Z 18 5.484 0.128 0.094 56.832
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.207 0.0337 0.781
HMC 8 5.394 3.32e-05 83.140
HMC 10 599.790 1.01e-73 216.356
HMC 12 628.482 2.01e-72 236.800
HMC 15 816.292 1.34e-66 372.523
HMC 18 1015.369 4.47e-77 401.194
SMC 5 1.538 0.132 0.510
SMC 8 0.545 0.589 0.196
SMC 10 -0.110 0.913 -0.033
SMC 12 0.227 0.822 0.071
SMC 15 -0.025 0.981 -0.010
SMC 18 -0.071 0.944 -0.025
Metro 5 3.220 0.00283 1.262
Metro 8 2.784 0.0117 8.468
Metro 10 3.679 0.00159 47.897
Metro 12 15.550 2.89e-12 216.312
Metro 15 773.758 1.47e-63 372.633
Metro 18 1062.125 3.02e-80 401.200
DEMetro_Z 5 3.802 0.000506 1.209
DEMetro_Z 8 2.827 0.0102 3.134
DEMetro_Z 10 3.435 0.00278 79.526
DEMetro_Z 12 7.711 2.88e-07 178.598
DEMetro_Z 15 19.031 7.8e-14 354.248
DEMetro_Z 18 10.453 2.56e-09 341.377
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.895 0.382 0.200
HMC_vs_SMC 1 5.363 3.56e-05 1.199
HMC_vs_SMC 2 568.725 1.15e-41 127.171
HMC_vs_SMC 3 626.417 1.84e-42 140.071
HMC_vs_SMC 4 787.495 2.38e-44 176.089
HMC_vs_SMC 5 1084.900 5.4e-47 242.591
Metro_vs_DEMetro_Z 0 0.143 0.887 0.032
Metro_vs_DEMetro_Z 1 1.545 0.139 0.346
Metro_vs_DEMetro_Z 2 -1.132 0.272 -0.253
Metro_vs_DEMetro_Z 3 1.294 0.211 0.289
Metro_vs_DEMetro_Z 4 0.987 0.336 0.221
Metro_vs_DEMetro_Z 5 1.833 0.0825 0.410
HMC_vs_Metro 0 -1.416 0.173 -0.317
HMC_vs_Metro 1 4.631 0.000182 1.035
HMC_vs_Metro 2 12.936 7.21e-11 2.893
HMC_vs_Metro 3 1.482 0.155 0.331
HMC_vs_Metro 4 -1.050 0.307 -0.235
HMC_vs_Metro 5 -0.105 0.917 -0.024
HMC_vs_DEMetro_Z 0 -1.188 0.25 -0.266
HMC_vs_DEMetro_Z 1 5.271 4.36e-05 1.179
HMC_vs_DEMetro_Z 2 5.907 1.09e-05 1.321
HMC_vs_DEMetro_Z 3 2.521 0.0208 0.564
HMC_vs_DEMetro_Z 4 0.977 0.341 0.219
HMC_vs_DEMetro_Z 5 1.834 0.0823 0.410
Metro_vs_SMC 0 1.867 0.0775 0.417
Metro_vs_SMC 1 2.842 0.0104 0.636
Metro_vs_SMC 2 3.662 0.00166 0.819
Metro_vs_SMC 3 15.494 3.11e-12 3.465
Metro_vs_SMC 4 760.805 4.58e-44 170.121
Metro_vs_SMC 5 1137.013 2.22e-47 254.244
DEMetro_Z_vs_SMC 0 1.882 0.0752 0.421
DEMetro_Z_vs_SMC 1 2.409 0.0263 0.539
DEMetro_Z_vs_SMC 2 3.435 0.00278 0.768
DEMetro_Z_vs_SMC 3 7.686 3.02e-07 1.719
DEMetro_Z_vs_SMC 4 19.022 7.9e-14 4.254
DEMetro_Z_vs_SMC 5 10.466 2.51e-09 2.340
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.087 0.048 0.050 0.781
HMC 8 6.151 0.081 0.073 83.140
HMC 10 17.659 0.119 0.081 216.356
HMC 12 25.471 0.161 0.107 236.800
HMC 15 39.766 0.204 0.106 372.523
HMC 18 57.267 0.197 0.142 401.194
SMC 5 0.074 0.048 0.050 0.510
SMC 8 0.095 0.081 0.073 0.196
SMC 10 0.116 0.119 0.081 -0.033
SMC 12 0.169 0.161 0.107 0.071
SMC 15 0.203 0.204 0.106 -0.010
SMC 18 0.193 0.197 0.142 -0.025
Metro 5 0.111 0.048 0.050 1.262
Metro 8 0.699 0.081 0.073 8.468
Metro 10 4.002 0.119 0.081 47.897
Metro 12 23.281 0.161 0.107 216.312
Metro 15 39.777 0.204 0.106 372.633
Metro 18 57.268 0.197 0.142 401.200
DEMetro_Z 5 0.108 0.048 0.050 1.209
DEMetro_Z 8 0.310 0.081 0.073 3.134
DEMetro_Z 10 6.566 0.119 0.081 79.526
DEMetro_Z 12 19.250 0.161 0.107 178.598
DEMetro_Z 15 37.825 0.204 0.106 354.248
DEMetro_Z 18 48.758 0.197 0.142 341.377
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.102 0.000403 2.628
HMC 8 7.510 4.21e-07 78.195
HMC 10 64.197 9.1e-25 84.322
HMC 12 66.483 5.23e-26 64.755
HMC 15 80.382 1.08e-26 106.958
HMC 18 71.315 9.82e-27 68.135
SMC 5 -0.664 0.511 -0.221
SMC 8 1.721 0.0945 0.691
SMC 10 0.404 0.689 0.123
SMC 12 -0.051 0.959 -0.014
SMC 15 1.423 0.164 0.585
SMC 18 -0.574 0.569 -0.163
Metro 5 3.754 0.000966 2.385
Metro 8 5.242 4.57e-05 22.249
Metro 10 5.744 1.53e-05 33.521
Metro 12 19.276 5.1e-14 61.645
Metro 15 77.906 2e-26 103.520
Metro 18 82.112 1.38e-28 70.729
DEMetro_Z 5 3.967 0.000536 2.362
DEMetro_Z 8 4.057 0.000654 10.186
DEMetro_Z 10 4.298 0.000387 36.570
DEMetro_Z 12 8.080 1.42e-07 50.027
DEMetro_Z 15 21.103 1.09e-14 103.330
DEMetro_Z 18 11.225 7.61e-10 58.789
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.028 0.978 0.006
Metro_vs_DEMetro_Z 1 2.210 0.0396 0.494
Metro_vs_DEMetro_Z 2 -0.264 0.795 -0.059
Metro_vs_DEMetro_Z 3 1.488 0.153 0.333
Metro_vs_DEMetro_Z 4 0.034 0.973 0.008
Metro_vs_DEMetro_Z 5 2.228 0.0381 0.498
DEMetro_Z_vs_SMC 0 3.886 0.000994 0.869
DEMetro_Z_vs_SMC 1 4.017 0.000737 0.898
DEMetro_Z_vs_SMC 2 4.302 0.000384 0.962
DEMetro_Z_vs_SMC 3 8.057 1.51e-07 1.802
DEMetro_Z_vs_SMC 4 21.214 1.09e-14 4.744
DEMetro_Z_vs_SMC 5 11.247 7.68e-10 2.515
HMC_vs_DEMetro_Z 0 0.316 0.755 0.071
HMC_vs_DEMetro_Z 1 6.678 2.19e-06 1.493
HMC_vs_DEMetro_Z 2 5.486 2.72e-05 1.227
HMC_vs_DEMetro_Z 3 2.383 0.0277 0.533
HMC_vs_DEMetro_Z 4 0.777 0.447 0.174
HMC_vs_DEMetro_Z 5 1.701 0.105 0.380
HMC_vs_Metro 0 0.291 0.774 0.065
HMC_vs_Metro 1 5.163 5.53e-05 1.155
HMC_vs_Metro 2 8.252 1.05e-07 1.845
HMC_vs_Metro 3 0.903 0.378 0.202
HMC_vs_Metro 4 1.569 0.133 0.351
HMC_vs_Metro 5 -2.044 0.0551 -0.457
HMC_vs_SMC 0 4.319 0.00037 0.966
HMC_vs_SMC 1 7.416 5.07e-07 1.658
HMC_vs_SMC 2 61.611 2.41e-23 13.777
HMC_vs_SMC 3 64.450 1.03e-23 14.411
HMC_vs_SMC 4 76.741 3.77e-25 17.160
HMC_vs_SMC 5 75.814 4.75e-25 16.952
Metro_vs_SMC 0 4.444 0.000279 0.994
Metro_vs_SMC 1 5.131 5.94e-05 1.147
Metro_vs_SMC 2 5.829 1.29e-05 1.303
Metro_vs_SMC 3 19.216 6.58e-14 4.297
Metro_vs_SMC 4 74.049 7.42e-25 16.558
Metro_vs_SMC 5 94.630 7.11e-27 21.160
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.119 0.057 0.024 2.628
HMC 8 1.635 0.060 0.020 78.195
HMC 10 3.094 0.068 0.036 84.322
HMC 12 3.850 0.097 0.058 64.755
HMC 15 4.821 0.090 0.044 106.958
HMC 18 5.602 0.132 0.080 68.135
SMC 5 0.051 0.057 0.024 -0.221
SMC 8 0.074 0.060 0.020 0.691
SMC 10 0.072 0.068 0.036 0.123
SMC 12 0.096 0.097 0.058 -0.014
SMC 15 0.116 0.090 0.044 0.585
SMC 18 0.119 0.132 0.080 -0.163
Metro 5 0.113 0.057 0.024 2.385
Metro 8 0.508 0.060 0.020 22.249
Metro 10 1.271 0.068 0.036 33.521
Metro 12 3.670 0.097 0.058 61.645
Metro 15 4.669 0.090 0.044 103.520
Metro 18 5.810 0.132 0.080 70.729
DEMetro_Z 5 0.113 0.057 0.024 2.362
DEMetro_Z 8 0.265 0.060 0.020 10.186
DEMetro_Z 10 1.381 0.068 0.036 36.570
DEMetro_Z 12 2.996 0.097 0.058 50.027
DEMetro_Z 15 4.660 0.090 0.044 103.330
DEMetro_Z 18 4.851 0.132 0.080 58.789
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.289 0.000275 3.101
HMC 8 7.599 3.54e-07 69.515
HMC 10 110.775 1.97e-32 83.728
HMC 12 142.487 7.86e-47 59.086
HMC 15 133.738 3.95e-34 102.683
HMC 18 137.170 4.05e-39 75.035
SMC 5 -0.242 0.81 -0.085
SMC 8 1.041 0.304 0.346
SMC 10 0.540 0.592 0.169
SMC 12 -0.506 0.616 -0.134
SMC 15 1.391 0.173 0.561
SMC 18 -0.412 0.683 -0.127
Metro 5 3.614 0.00143 2.492
Metro 8 5.139 5.7e-05 18.851
Metro 10 6.120 6.86e-06 32.124
Metro 12 22.310 2.99e-15 55.423
Metro 15 124.114 7.35e-33 101.576
Metro 18 145.920 5.38e-41 75.575
DEMetro_Z 5 3.524 0.0018 2.481
DEMetro_Z 8 3.542 0.00214 9.008
DEMetro_Z 10 4.318 0.00037 36.272
DEMetro_Z 12 8.210 1.11e-07 45.552
DEMetro_Z 15 22.216 4.17e-15 98.917
DEMetro_Z 18 11.334 6.53e-10 65.844
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.247 0.00424 0.726
DEMetro_Z_vs_SMC 1 3.537 0.0022 0.791
DEMetro_Z_vs_SMC 2 4.314 0.000375 0.965
DEMetro_Z_vs_SMC 3 8.204 1.15e-07 1.835
DEMetro_Z_vs_SMC 4 22.441 3.89e-15 5.018
DEMetro_Z_vs_SMC 5 11.329 6.8e-10 2.533
HMC_vs_Metro 0 0.665 0.514 0.149
HMC_vs_Metro 1 5.442 2.99e-05 1.217
HMC_vs_Metro 2 9.522 1.15e-08 2.129
HMC_vs_Metro 3 1.406 0.176 0.314
HMC_vs_Metro 4 1.487 0.153 0.333
HMC_vs_Metro 5 -0.946 0.356 -0.211
Metro_vs_DEMetro_Z 0 0.011 0.991 0.002
Metro_vs_DEMetro_Z 1 1.968 0.0638 0.440
Metro_vs_DEMetro_Z 2 -0.369 0.717 -0.082
Metro_vs_DEMetro_Z 3 1.489 0.153 0.333
Metro_vs_DEMetro_Z 4 0.539 0.596 0.120
Metro_vs_DEMetro_Z 5 1.636 0.118 0.366
HMC_vs_SMC 0 4.264 0.00042 0.953
HMC_vs_SMC 1 7.537 4.02e-07 1.685
HMC_vs_SMC 2 103.547 1.29e-27 23.154
HMC_vs_SMC 3 149.763 1.17e-30 33.488
HMC_vs_SMC 4 111.375 3.24e-28 24.904
HMC_vs_SMC 5 144.120 2.43e-30 32.226
Metro_vs_SMC 0 3.952 0.000856 0.884
Metro_vs_SMC 1 5.092 6.48e-05 1.139
Metro_vs_SMC 2 6.213 5.73e-06 1.389
Metro_vs_SMC 3 22.478 3.77e-15 5.026
Metro_vs_SMC 4 108.659 5.17e-28 24.297
Metro_vs_SMC 5 131.901 1.31e-29 29.494
HMC_vs_DEMetro_Z 0 0.623 0.541 0.139
HMC_vs_DEMetro_Z 1 6.711 2.05e-06 1.501
HMC_vs_DEMetro_Z 2 5.451 2.93e-05 1.219
HMC_vs_DEMetro_Z 3 2.424 0.0255 0.542
HMC_vs_DEMetro_Z 4 0.795 0.436 0.178
HMC_vs_DEMetro_Z 5 1.552 0.137 0.347
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.037 0.015 0.007 3.101
HMC 8 0.402 0.012 0.006 69.515
HMC 10 0.621 0.011 0.007 83.728
HMC 12 0.611 0.014 0.010 59.086
HMC 15 0.616 0.010 0.006 102.683
HMC 18 0.613 0.012 0.008 75.035
SMC 5 0.014 0.015 0.007 -0.085
SMC 8 0.014 0.012 0.006 0.346
SMC 10 0.012 0.011 0.007 0.169
SMC 12 0.013 0.014 0.010 -0.134
SMC 15 0.013 0.010 0.006 0.561
SMC 18 0.011 0.012 0.008 -0.127
Metro 5 0.032 0.015 0.007 2.492
Metro 8 0.118 0.012 0.006 18.851
Metro 10 0.245 0.011 0.007 32.124
Metro 12 0.574 0.014 0.010 55.423
Metro 15 0.609 0.010 0.006 101.576
Metro 18 0.618 0.012 0.008 75.575
DEMetro_Z 5 0.032 0.015 0.007 2.481
DEMetro_Z 8 0.063 0.012 0.006 9.008
DEMetro_Z 10 0.275 0.011 0.007 36.272
DEMetro_Z 12 0.474 0.014 0.010 45.552
DEMetro_Z 15 0.594 0.010 0.006 98.917
DEMetro_Z 18 0.540 0.012 0.008 65.844
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Varying_Mode_Distance_with_high_Dimension (Mixture, mm, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 1.912 0.0703 2.755
HMC 8 6.458 3.39e-06 34.732
HMC 10 4.713 0.00015 28.317
HMC 12 5.449 2.93e-05 39.830
HMC 15 6.260 5.17e-06 61.815
HMC 18 4.563 0.000212 35.542
SMC 5 0.265 0.793 0.143
SMC 8 0.464 0.645 0.138
SMC 10 0.578 0.567 0.179
SMC 12 -0.757 0.454 -0.207
SMC 15 1.537 0.134 0.641
SMC 18 1.413 0.166 0.474
Metro 5 10.570 5.26e-10 9.269
Metro 8 5.424 2.96e-05 13.980
Metro 10 5.119 6.05e-05 29.470
Metro 12 5.732 1.58e-05 36.701
Metro 15 6.414 3.75e-06 62.426
Metro 18 4.673 0.000165 35.916
DEMetro_Z 5 43.088 2.05e-20 2583.040
DEMetro_Z 8 30.152 1.64e-17 826.679
DEMetro_Z 10 42.608 2.51e-20 831.650
DEMetro_Z 12 40.636 6.08e-20 591.030
DEMetro_Z 15 29.417 2.59e-17 687.442
DEMetro_Z 18 26.811 1.44e-16 380.403
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -43.079 2.06e-20 -9.633
HMC_vs_DEMetro_Z 1 -27.539 8.88e-17 -6.158
HMC_vs_DEMetro_Z 2 -38.919 1.39e-19 -8.703
HMC_vs_DEMetro_Z 3 -37.789 2.42e-19 -8.450
HMC_vs_DEMetro_Z 4 -28.291 5.39e-17 -6.326
HMC_vs_DEMetro_Z 5 -24.844 5.98e-16 -5.555
Metro_vs_SMC 0 8.225 1.11e-07 1.839
Metro_vs_SMC 1 5.306 4.03e-05 1.186
Metro_vs_SMC 2 5.077 6.69e-05 1.135
Metro_vs_SMC 3 5.786 1.42e-05 1.294
Metro_vs_SMC 4 6.337 4.42e-06 1.417
Metro_vs_SMC 5 4.657 0.000172 1.041
Metro_vs_DEMetro_Z 0 -42.896 2.23e-20 -9.592
Metro_vs_DEMetro_Z 1 -30.415 1.4e-17 -6.801
Metro_vs_DEMetro_Z 2 -38.853 1.43e-19 -8.688
Metro_vs_DEMetro_Z 3 -33.498 2.31e-18 -7.490
Metro_vs_DEMetro_Z 4 -28.312 5.31e-17 -6.331
Metro_vs_DEMetro_Z 5 -24.867 5.88e-16 -5.561
HMC_vs_Metro 0 -4.854 0.00011 -1.085
HMC_vs_Metro 1 3.169 0.00505 0.709
HMC_vs_Metro 2 -0.162 0.873 -0.036
HMC_vs_Metro 3 0.773 0.449 0.173
HMC_vs_Metro 4 -2.946 0.00829 -0.659
HMC_vs_Metro 5 -2.522 0.0208 -0.564
HMC_vs_SMC 0 1.753 0.0957 0.392
HMC_vs_SMC 1 6.507 3.11e-06 1.455
HMC_vs_SMC 2 4.669 0.000167 1.044
HMC_vs_SMC 3 5.487 2.71e-05 1.227
HMC_vs_SMC 4 6.184 6.09e-06 1.383
HMC_vs_SMC 5 4.546 0.000221 1.016
DEMetro_Z_vs_SMC 0 43.025 2.11e-20 9.621
DEMetro_Z_vs_SMC 1 30.059 1.74e-17 6.721
DEMetro_Z_vs_SMC 2 42.802 2.33e-20 9.571
DEMetro_Z_vs_SMC 3 40.510 6.55e-20 9.058
DEMetro_Z_vs_SMC 4 29.293 2.82e-17 6.550
DEMetro_Z_vs_SMC 5 26.800 1.47e-16 5.993
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.031 0.024 0.003 2.755
HMC 8 0.313 0.028 0.008 34.732
HMC 10 0.260 0.029 0.008 28.317
HMC 12 0.468 0.033 0.011 39.830
HMC 15 0.629 0.032 0.010 61.815
HMC 18 0.678 0.038 0.018 35.542
SMC 5 0.024 0.024 0.003 0.143
SMC 8 0.030 0.028 0.008 0.138
SMC 10 0.031 0.029 0.008 0.179
SMC 12 0.031 0.033 0.011 -0.207
SMC 15 0.038 0.032 0.010 0.641
SMC 18 0.046 0.038 0.018 0.474
Metro 5 0.048 0.024 0.003 9.269
Metro 8 0.143 0.028 0.008 13.980
Metro 10 0.270 0.029 0.008 29.470
Metro 12 0.434 0.033 0.011 36.701
Metro 15 0.635 0.032 0.010 62.426
Metro 18 0.685 0.038 0.018 35.916
DEMetro_Z 5 6.848 0.024 0.003 2583.040
DEMetro_Z 8 6.807 0.028 0.008 826.679
DEMetro_Z 10 6.811 0.029 0.008 831.650
DEMetro_Z 12 6.476 0.033 0.011 591.030
DEMetro_Z 15 6.671 0.032 0.010 687.442
DEMetro_Z 18 6.893 0.038 0.018 380.403
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.883 0.00701 0.760
HMC 8 4.407 0.000302 34.003
HMC 10 4.914 9.58e-05 32.566
HMC 12 3.859 0.00106 75.287
HMC 15 4.178 0.000511 114.299
HMC 18 3.544 0.00217 164.615
SMC 5 2.045 0.0486 0.559
SMC 8 0.997 0.325 0.290
SMC 10 1.897 0.0676 0.874
SMC 12 1.176 0.248 0.497
SMC 15 2.244 0.0322 0.989
SMC 18 1.890 0.0692 0.952
Metro 5 6.034 6.58e-07 2.225
Metro 8 3.384 0.00303 6.593
Metro 10 2.762 0.0124 30.800
Metro 12 3.746 0.00137 63.048
Metro 15 4.226 0.000458 115.193
Metro 18 3.561 0.00208 165.106
DEMetro_Z 5 28.858 3.73e-17 17962.934
DEMetro_Z 8 26.601 1.69e-16 8041.650
DEMetro_Z 10 32.474 4.13e-18 8995.026
DEMetro_Z 12 28.583 4.45e-17 6617.466
DEMetro_Z 15 30.542 1.3e-17 6171.854
DEMetro_Z 18 27.356 1.01e-16 6883.164
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.859 0.401 0.192
HMC_vs_SMC 1 4.389 0.000316 0.981
HMC_vs_SMC 2 4.748 0.00014 1.062
HMC_vs_SMC 3 3.858 0.00106 0.863
HMC_vs_SMC 4 4.116 0.000588 0.920
HMC_vs_SMC 5 3.523 0.00227 0.788
Metro_vs_DEMetro_Z 0 -28.855 3.73e-17 -6.452
Metro_vs_DEMetro_Z 1 -26.586 1.71e-16 -5.945
Metro_vs_DEMetro_Z 2 -32.387 4.34e-18 -7.242
Metro_vs_DEMetro_Z 3 -28.419 4.96e-17 -6.355
Metro_vs_DEMetro_Z 4 -30.140 1.66e-17 -6.740
Metro_vs_DEMetro_Z 5 -24.953 5.51e-16 -5.580
HMC_vs_Metro 0 -4.416 0.000297 -0.988
HMC_vs_Metro 1 3.272 0.00401 0.732
HMC_vs_Metro 2 0.155 0.878 0.035
HMC_vs_Metro 3 1.131 0.272 0.253
HMC_vs_Metro 4 -1.636 0.118 -0.366
HMC_vs_Metro 5 -0.632 0.535 -0.141
HMC_vs_DEMetro_Z 0 -28.854 3.74e-17 -6.452
HMC_vs_DEMetro_Z 1 -26.269 2.13e-16 -5.874
HMC_vs_DEMetro_Z 2 -32.665 3.7e-18 -7.304
HMC_vs_DEMetro_Z 3 -29.080 3.23e-17 -6.502
HMC_vs_DEMetro_Z 4 -30.137 1.66e-17 -6.739
HMC_vs_DEMetro_Z 5 -24.952 5.52e-16 -5.579
Metro_vs_SMC 0 4.831 0.000116 1.080
Metro_vs_SMC 1 3.148 0.0053 0.704
Metro_vs_SMC 2 2.670 0.0151 0.597
Metro_vs_SMC 3 3.755 0.00134 0.840
Metro_vs_SMC 4 4.163 0.000528 0.931
Metro_vs_SMC 5 3.541 0.00218 0.792
DEMetro_Z_vs_SMC 0 28.858 3.73e-17 6.453
DEMetro_Z_vs_SMC 1 26.597 1.69e-16 5.947
DEMetro_Z_vs_SMC 2 32.468 4.14e-18 7.260
DEMetro_Z_vs_SMC 3 28.579 4.47e-17 6.390
DEMetro_Z_vs_SMC 4 30.549 1.29e-17 6.831
DEMetro_Z_vs_SMC 5 27.359 1e-16 6.118
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.046 0.039 0.009 0.760
HMC 8 0.746 0.048 0.021 34.003
HMC 10 0.653 0.049 0.019 32.566
HMC 12 1.903 0.053 0.025 75.287
HMC 15 3.105 0.053 0.027 114.299
HMC 18 4.456 0.057 0.027 164.615
SMC 5 0.044 0.039 0.009 0.559
SMC 8 0.054 0.048 0.021 0.290
SMC 10 0.065 0.049 0.019 0.874
SMC 12 0.066 0.053 0.025 0.497
SMC 15 0.079 0.053 0.027 0.989
SMC 18 0.083 0.057 0.027 0.952
Metro 5 0.059 0.039 0.009 2.225
Metro 8 0.183 0.048 0.021 6.593
Metro 10 0.620 0.049 0.019 30.800
Metro 12 1.602 0.053 0.025 63.048
Metro 15 3.129 0.053 0.027 115.193
Metro 18 4.469 0.057 0.027 165.106
DEMetro_Z 5 167.859 0.039 0.009 17962.934
DEMetro_Z 8 165.208 0.048 0.021 8041.650
DEMetro_Z 10 166.831 0.049 0.019 8995.026
DEMetro_Z 12 162.632 0.053 0.025 6617.466
DEMetro_Z 15 164.867 0.053 0.027 6171.854
DEMetro_Z 18 183.980 0.057 0.027 6883.164
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.073 0.0514 3.280
HMC 8 6.459 3.4e-06 45.670
HMC 10 4.765 0.000134 35.161
HMC 12 5.536 2.43e-05 48.249
HMC 15 6.315 4.62e-06 75.208
HMC 18 4.564 0.000212 41.610
SMC 5 0.838 0.408 0.359
SMC 8 0.957 0.345 0.298
SMC 10 0.862 0.394 0.262
SMC 12 -0.297 0.768 -0.082
SMC 15 1.850 0.0735 0.777
SMC 18 1.707 0.096 0.561
Metro 5 11.051 2.36e-10 9.752
Metro 8 5.141 5.67e-05 18.227
Metro 10 4.953 8.79e-05 37.134
Metro 12 5.881 1.15e-05 45.556
Metro 15 6.458 3.43e-06 78.153
Metro 18 4.714 0.000151 43.349
DEMetro_Z 5 53.747 3.18e-22 5686.603
DEMetro_Z 8 44.030 1.36e-20 2027.008
DEMetro_Z 10 74.010 7.45e-25 1983.290
DEMetro_Z 12 46.966 4.03e-21 1358.676
DEMetro_Z 15 58.811 5.77e-23 1596.548
DEMetro_Z 18 55.965 1.46e-22 856.754
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -53.459 3.52e-22 -11.954
Metro_vs_DEMetro_Z 1 -43.789 1.51e-20 -9.791
Metro_vs_DEMetro_Z 2 -72.270 1.18e-24 -16.160
Metro_vs_DEMetro_Z 3 -43.913 1.44e-20 -9.819
Metro_vs_DEMetro_Z 4 -55.627 1.66e-22 -12.439
Metro_vs_DEMetro_Z 5 -44.968 9.18e-21 -10.055
DEMetro_Z_vs_SMC 0 53.758 3.17e-22 12.021
DEMetro_Z_vs_SMC 1 43.950 1.41e-20 9.828
DEMetro_Z_vs_SMC 2 74.130 7.27e-25 16.576
DEMetro_Z_vs_SMC 3 46.927 4.11e-21 10.493
DEMetro_Z_vs_SMC 4 58.658 6.1e-23 13.116
DEMetro_Z_vs_SMC 5 55.923 1.5e-22 12.505
HMC_vs_DEMetro_Z 0 -53.664 3.27e-22 -12.000
HMC_vs_DEMetro_Z 1 -40.771 5.8e-20 -9.117
HMC_vs_DEMetro_Z 2 -80.321 1.59e-25 -17.960
HMC_vs_DEMetro_Z 3 -46.575 4.74e-21 -10.414
HMC_vs_DEMetro_Z 4 -54.952 2.09e-22 -12.288
HMC_vs_DEMetro_Z 5 -45.218 8.27e-21 -10.111
HMC_vs_Metro 0 -4.171 0.000518 -0.933
HMC_vs_Metro 1 3.141 0.00538 0.702
HMC_vs_Metro 2 -0.216 0.831 -0.048
HMC_vs_Metro 3 0.567 0.577 0.127
HMC_vs_Metro 4 -2.494 0.022 -0.558
HMC_vs_Metro 5 -2.010 0.0589 -0.449
HMC_vs_SMC 0 1.825 0.0837 0.408
HMC_vs_SMC 1 6.484 3.26e-06 1.450
HMC_vs_SMC 2 4.701 0.000156 1.051
HMC_vs_SMC 3 5.557 2.33e-05 1.243
HMC_vs_SMC 4 6.238 5.44e-06 1.395
HMC_vs_SMC 5 4.542 0.000223 1.016
Metro_vs_SMC 0 9.002 2.78e-08 2.013
Metro_vs_SMC 1 4.971 8.48e-05 1.112
Metro_vs_SMC 2 4.909 9.75e-05 1.098
Metro_vs_SMC 3 5.914 1.08e-05 1.322
Metro_vs_SMC 4 6.385 4e-06 1.428
Metro_vs_SMC 5 4.694 0.000158 1.050
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.037 0.031 0.002 3.280
HMC 8 0.258 0.035 0.005 45.670
HMC 10 0.214 0.036 0.005 35.161
HMC 12 0.381 0.040 0.007 48.249
HMC 15 0.503 0.040 0.006 75.208
HMC 18 0.544 0.044 0.012 41.610
SMC 5 0.032 0.031 0.002 0.359
SMC 8 0.036 0.035 0.005 0.298
SMC 10 0.038 0.036 0.005 0.262
SMC 12 0.039 0.040 0.007 -0.082
SMC 15 0.045 0.040 0.006 0.777
SMC 18 0.051 0.044 0.012 0.561
Metro 5 0.048 0.031 0.002 9.752
Metro 8 0.124 0.035 0.005 18.227
Metro 10 0.224 0.036 0.005 37.134
Metro 12 0.362 0.040 0.007 45.556
Metro 15 0.522 0.040 0.006 78.153
Metro 18 0.565 0.044 0.012 43.349
DEMetro_Z 5 10.112 0.031 0.002 5686.603
DEMetro_Z 8 9.938 0.035 0.005 2027.008
DEMetro_Z 10 10.068 0.036 0.005 1983.290
DEMetro_Z 12 9.665 0.040 0.007 1358.676
DEMetro_Z 15 9.881 0.040 0.006 1596.548
DEMetro_Z 18 10.340 0.044 0.012 856.754
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.429 0.0246 3.167
HMC 8 6.338 4.37e-06 43.513
HMC 10 4.740 0.000142 31.864
HMC 12 5.419 3.13e-05 47.476
HMC 15 6.349 4.3e-06 71.149
HMC 18 4.584 0.000202 43.579
SMC 5 1.615 0.117 0.734
SMC 8 0.957 0.344 0.291
SMC 10 1.020 0.314 0.311
SMC 12 -0.454 0.652 -0.129
SMC 15 1.739 0.0917 0.738
SMC 18 1.088 0.284 0.364
Metro 5 11.304 1.26e-10 9.345
Metro 8 5.412 3.09e-05 17.373
Metro 10 4.886 0.000102 33.136
Metro 12 5.602 2.1e-05 43.412
Metro 15 6.427 3.66e-06 71.909
Metro 18 4.668 0.000167 44.296
DEMetro_Z 5 118.922 6.21e-29 433.276
DEMetro_Z 8 64.121 6.99e-24 189.913
DEMetro_Z 10 60.526 2.15e-23 183.237
DEMetro_Z 12 81.094 3.14e-26 146.717
DEMetro_Z 15 68.599 1.68e-24 180.149
DEMetro_Z 18 95.045 1.98e-28 114.669
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 114.987 1.77e-28 25.712
DEMetro_Z_vs_SMC 1 64.510 1.01e-23 14.425
DEMetro_Z_vs_SMC 2 60.131 3.82e-23 13.446
DEMetro_Z_vs_SMC 3 79.581 1.9e-25 17.795
DEMetro_Z_vs_SMC 4 65.247 8.15e-24 14.590
DEMetro_Z_vs_SMC 5 97.363 4.15e-27 21.771
HMC_vs_Metro 0 -4.541 0.000224 -1.015
HMC_vs_Metro 1 3.147 0.00531 0.704
HMC_vs_Metro 2 -0.154 0.879 -0.035
HMC_vs_Metro 3 0.852 0.405 0.191
HMC_vs_Metro 4 -1.115 0.279 -0.249
HMC_vs_Metro 5 -1.697 0.106 -0.380
Metro_vs_DEMetro_Z 0 -112.302 2.77e-28 -25.112
Metro_vs_DEMetro_Z 1 -45.527 7.28e-21 -10.180
Metro_vs_DEMetro_Z 2 -18.468 1.35e-13 -4.130
Metro_vs_DEMetro_Z 3 -12.660 1.04e-10 -2.831
Metro_vs_DEMetro_Z 4 -9.645 9.39e-09 -2.157
Metro_vs_DEMetro_Z 5 -7.565 3.8e-07 -1.692
HMC_vs_SMC 0 1.876 0.0762 0.419
HMC_vs_SMC 1 6.333 4.46e-06 1.416
HMC_vs_SMC 2 4.675 0.000165 1.045
HMC_vs_SMC 3 5.452 2.93e-05 1.219
HMC_vs_SMC 4 6.270 5.09e-06 1.402
HMC_vs_SMC 5 4.573 0.000208 1.023
Metro_vs_SMC 0 8.966 2.96e-08 2.005
Metro_vs_SMC 1 5.249 4.57e-05 1.174
Metro_vs_SMC 2 4.830 0.000116 1.080
Metro_vs_SMC 3 5.649 1.91e-05 1.263
Metro_vs_SMC 4 6.345 4.35e-06 1.419
Metro_vs_SMC 5 4.658 0.000172 1.041
HMC_vs_DEMetro_Z 0 -107.477 6.36e-28 -24.033
HMC_vs_DEMetro_Z 1 -17.258 4.56e-13 -3.859
HMC_vs_DEMetro_Z 2 -17.307 4.34e-13 -3.870
HMC_vs_DEMetro_Z 3 -11.047 1.03e-09 -2.470
HMC_vs_DEMetro_Z 4 -9.660 9.17e-09 -2.160
HMC_vs_DEMetro_Z 5 -7.615 3.46e-07 -1.703
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.018 0.013 0.001 3.167
HMC 8 0.144 0.014 0.003 43.513
HMC 10 0.113 0.014 0.003 31.864
HMC 12 0.194 0.015 0.004 47.476
HMC 15 0.231 0.012 0.003 71.149
HMC 18 0.225 0.013 0.005 43.579
SMC 5 0.014 0.013 0.001 0.734
SMC 8 0.015 0.014 0.003 0.291
SMC 10 0.015 0.014 0.003 0.311
SMC 12 0.014 0.015 0.004 -0.129
SMC 15 0.015 0.012 0.003 0.738
SMC 18 0.015 0.013 0.005 0.364
Metro 5 0.026 0.013 0.001 9.345
Metro 8 0.066 0.014 0.003 17.373
Metro 10 0.117 0.014 0.003 33.136
Metro 12 0.179 0.015 0.004 43.412
Metro 15 0.233 0.012 0.003 71.909
Metro 18 0.229 0.013 0.005 44.296
DEMetro_Z 5 0.577 0.013 0.001 433.276
DEMetro_Z 8 0.580 0.014 0.003 189.913
DEMetro_Z 10 0.581 0.014 0.003 183.237
DEMetro_Z 12 0.569 0.015 0.004 146.717
DEMetro_Z 15 0.566 0.012 0.003 180.149
DEMetro_Z 18 0.572 0.013 0.005 114.669
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.505 0.0204 2.294
HMC 8 7.741 2.69e-07 54.973
HMC 10 277.932 2.78e-58 109.440
HMC 12 280.798 6.31e-63 98.020
HMC 15 225.336 2.35e-42 138.777
HMC 18 202.264 9.06e-50 88.752
SMC 5 1.247 0.221 0.497
SMC 8 -1.558 0.128 -0.450
SMC 10 0.833 0.41 0.282
SMC 12 -1.866 0.0699 -0.558
SMC 15 0.859 0.397 0.370
SMC 18 1.067 0.293 0.421
Metro 5 7.771 1.66e-07 9.658
Metro 8 5.339 3.63e-05 17.163
Metro 10 5.035 7.32e-05 42.497
Metro 12 17.283 4.13e-13 86.730
Metro 15 224.896 2.59e-42 138.677
Metro 18 198.760 5.53e-49 88.673
DEMetro_Z 5 20.542 1.96e-14 4008.726
DEMetro_Z 8 25.221 4.52e-16 1230.166
DEMetro_Z 10 30.005 1.8e-17 1496.788
DEMetro_Z 12 28.737 4.02e-17 1009.386
DEMetro_Z 15 20.388 2.24e-14 1145.082
DEMetro_Z 18 30.489 1.33e-17 613.855
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -20.517 2e-14 -4.588
HMC_vs_DEMetro_Z 1 -23.566 1.58e-15 -5.269
HMC_vs_DEMetro_Z 2 -27.845 7.24e-17 -6.226
HMC_vs_DEMetro_Z 3 -25.911 2.75e-16 -5.794
HMC_vs_DEMetro_Z 4 -17.909 2.35e-13 -4.005
HMC_vs_DEMetro_Z 5 -26.049 2.49e-16 -5.825
Metro_vs_SMC 0 7.577 3.72e-07 1.694
Metro_vs_SMC 1 5.485 2.73e-05 1.226
Metro_vs_SMC 2 4.997 8.01e-05 1.117
Metro_vs_SMC 3 17.580 3.27e-13 3.931
Metro_vs_SMC 4 218.020 9.38e-34 48.751
Metro_vs_SMC 5 184.201 2.3e-32 41.189
Metro_vs_DEMetro_Z 0 -20.440 2.14e-14 -4.570
Metro_vs_DEMetro_Z 1 -24.736 6.48e-16 -5.531
Metro_vs_DEMetro_Z 2 -29.580 2.35e-17 -6.614
Metro_vs_DEMetro_Z 3 -25.219 4.53e-16 -5.639
Metro_vs_DEMetro_Z 4 -17.923 2.31e-13 -4.008
Metro_vs_DEMetro_Z 5 -26.088 2.42e-16 -5.834
HMC_vs_Metro 0 -4.790 0.000127 -1.071
HMC_vs_Metro 1 5.135 5.89e-05 1.148
HMC_vs_Metro 2 8.028 1.59e-07 1.795
HMC_vs_Metro 3 2.257 0.036 0.505
HMC_vs_Metro 4 0.744 0.466 0.166
HMC_vs_Metro 5 1.243 0.229 0.278
HMC_vs_SMC 0 1.893 0.0737 0.423
HMC_vs_SMC 1 7.797 2.45e-07 1.744
HMC_vs_SMC 2 275.816 1.08e-35 61.674
HMC_vs_SMC 3 342.612 1.75e-37 76.610
HMC_vs_SMC 4 218.875 8.7e-34 48.942
HMC_vs_SMC 5 179.093 3.93e-32 40.046
DEMetro_Z_vs_SMC 0 20.538 1.97e-14 4.592
DEMetro_Z_vs_SMC 1 25.242 4.46e-16 5.644
DEMetro_Z_vs_SMC 2 30.006 1.8e-17 6.710
DEMetro_Z_vs_SMC 3 28.725 4.06e-17 6.423
DEMetro_Z_vs_SMC 4 20.352 2.32e-14 4.551
DEMetro_Z_vs_SMC 5 30.591 1.26e-17 6.840
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.030 0.024 0.003 2.294
HMC 8 0.479 0.028 0.008 54.973
HMC 10 0.922 0.029 0.008 109.440
HMC 12 1.102 0.033 0.011 98.020
HMC 15 1.372 0.032 0.010 138.777
HMC 18 1.637 0.038 0.018 88.752
SMC 5 0.025 0.024 0.003 0.497
SMC 8 0.025 0.028 0.008 -0.450
SMC 10 0.032 0.029 0.008 0.282
SMC 12 0.027 0.033 0.011 -0.558
SMC 15 0.035 0.032 0.010 0.370
SMC 18 0.045 0.038 0.018 0.421
Metro 5 0.049 0.024 0.003 9.658
Metro 8 0.169 0.028 0.008 17.163
Metro 10 0.376 0.029 0.008 42.497
Metro 12 0.979 0.033 0.011 86.730
Metro 15 1.371 0.032 0.010 138.677
Metro 18 1.636 0.038 0.018 88.673
DEMetro_Z 5 10.614 0.024 0.003 4008.726
DEMetro_Z 8 10.115 0.028 0.008 1230.166
DEMetro_Z 10 12.236 0.029 0.008 1496.788
DEMetro_Z 12 11.036 0.033 0.011 1009.386
DEMetro_Z 15 11.091 0.032 0.010 1145.082
DEMetro_Z 18 11.100 0.038 0.018 613.855
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.502 0.0182 0.634
HMC 8 5.825 1.3e-05 75.922
HMC 10 470.056 8.94e-55 243.979
HMC 12 717.825 1.7e-75 264.721
HMC 15 747.176 1.07e-60 383.077
HMC 18 1213.905 5.14e-72 551.127
SMC 5 -1.330 0.192 -0.378
SMC 8 -1.934 0.065 -0.461
SMC 10 0.741 0.463 0.227
SMC 12 -0.485 0.631 -0.135
SMC 15 1.865 0.0715 0.787
SMC 18 1.479 0.148 0.557
Metro 5 6.206 3.04e-07 2.045
Metro 8 2.781 0.0118 9.581
Metro 10 3.451 0.00268 65.644
Metro 12 12.050 2.41e-10 221.909
Metro 15 748.563 8.93e-61 383.201
Metro 18 1191.530 7.43e-71 551.047
DEMetro_Z 5 16.154 1.48e-12 2130.037
DEMetro_Z 8 17.224 4.73e-13 1121.562
DEMetro_Z 10 11.197 8.27e-10 1186.216
DEMetro_Z 12 12.516 1.27e-10 852.201
DEMetro_Z 15 19.452 5.27e-14 802.504
DEMetro_Z 18 19.532 4.89e-14 978.110
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 4.914 9.63e-05 1.099
HMC_vs_SMC 1 5.874 1.17e-05 1.313
HMC_vs_SMC 2 497.707 1.45e-40 111.291
HMC_vs_SMC 3 692.991 2.7e-43 154.958
HMC_vs_SMC 4 893.937 2.14e-45 199.890
HMC_vs_SMC 5 1057.127 8.84e-47 236.381
Metro_vs_DEMetro_Z 0 -16.145 1.5e-12 -3.610
Metro_vs_DEMetro_Z 1 -17.022 5.84e-13 -3.806
Metro_vs_DEMetro_Z 2 -10.105 4.44e-09 -2.260
Metro_vs_DEMetro_Z 3 -9.009 2.75e-08 -2.014
Metro_vs_DEMetro_Z 4 -10.191 3.88e-09 -2.279
Metro_vs_DEMetro_Z 5 -8.530 6.39e-08 -1.907
HMC_vs_Metro 0 -5.903 1.1e-05 -1.320
HMC_vs_Metro 1 5.062 6.92e-05 1.132
HMC_vs_Metro 2 9.373 1.48e-08 2.096
HMC_vs_Metro 3 2.310 0.0323 0.517
HMC_vs_Metro 4 -1.264 0.221 -0.283
HMC_vs_Metro 5 0.737 0.47 0.165
HMC_vs_DEMetro_Z 0 -16.154 1.48e-12 -3.612
HMC_vs_DEMetro_Z 1 -16.229 1.37e-12 -3.629
HMC_vs_DEMetro_Z 2 -8.904 3.3e-08 -1.991
HMC_vs_DEMetro_Z 3 -8.631 5.33e-08 -1.930
HMC_vs_DEMetro_Z 4 -10.200 3.82e-09 -2.281
HMC_vs_DEMetro_Z 5 -8.525 6.44e-08 -1.906
Metro_vs_SMC 0 8.150 1.27e-07 1.822
Metro_vs_SMC 1 2.950 0.00823 0.660
Metro_vs_SMC 2 3.447 0.0027 0.771
Metro_vs_SMC 3 12.070 2.35e-10 2.699
Metro_vs_SMC 4 902.145 1.8e-45 201.726
Metro_vs_SMC 5 1047.650 1.05e-46 234.262
DEMetro_Z_vs_SMC 0 16.162 1.47e-12 3.614
DEMetro_Z_vs_SMC 1 17.239 4.65e-13 3.855
DEMetro_Z_vs_SMC 2 11.194 8.31e-10 2.503
DEMetro_Z_vs_SMC 3 12.520 1.26e-10 2.800
DEMetro_Z_vs_SMC 4 19.451 5.28e-14 4.349
DEMetro_Z_vs_SMC 5 19.525 4.93e-14 4.366
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.045 0.039 0.009 0.634
HMC 8 1.607 0.048 0.021 75.922
HMC 10 4.573 0.049 0.019 243.979
HMC 12 6.557 0.053 0.025 264.721
HMC 15 10.283 0.053 0.027 383.077
HMC 18 14.784 0.057 0.027 551.127
SMC 5 0.035 0.039 0.009 -0.378
SMC 8 0.039 0.048 0.021 -0.461
SMC 10 0.053 0.049 0.019 0.227
SMC 12 0.050 0.053 0.025 -0.135
SMC 15 0.074 0.053 0.027 0.787
SMC 18 0.072 0.057 0.027 0.557
Metro 5 0.058 0.039 0.009 2.045
Metro 8 0.245 0.048 0.021 9.581
Metro 10 1.266 0.049 0.019 65.644
Metro 12 5.505 0.053 0.025 221.909
Metro 15 10.286 0.053 0.027 383.201
Metro 18 14.781 0.057 0.027 551.047
DEMetro_Z 5 19.939 0.039 0.009 2130.037
DEMetro_Z 8 23.083 0.048 0.021 1121.562
DEMetro_Z 10 22.043 0.049 0.019 1186.216
DEMetro_Z 12 20.990 0.053 0.025 852.201
DEMetro_Z 15 21.483 0.053 0.027 802.504
DEMetro_Z 18 26.193 0.057 0.027 978.110
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.271 0.00353 2.802
HMC 8 7.427 4.93e-07 72.986
HMC 10 121.235 1.02e-30 140.526
HMC 12 102.063 3.97e-29 120.570
HMC 15 68.755 1.5e-24 172.027
HMC 18 99.200 3.3e-29 106.989
SMC 5 0.851 0.401 0.319
SMC 8 -1.369 0.18 -0.392
SMC 10 0.977 0.335 0.331
SMC 12 -1.658 0.106 -0.484
SMC 15 0.962 0.344 0.463
SMC 18 1.067 0.293 0.425
Metro 5 8.027 1.04e-07 10.394
Metro 8 5.056 6.91e-05 21.891
Metro 10 4.998 7.96e-05 52.868
Metro 12 16.558 9.15e-13 105.001
Metro 15 109.688 5.1e-29 172.976
Metro 18 81.425 7.67e-27 106.810
DEMetro_Z 5 19.638 4.44e-14 4983.352
DEMetro_Z 8 23.879 1.24e-15 1706.816
DEMetro_Z 10 32.464 4.15e-18 1986.233
DEMetro_Z 12 28.736 4.03e-17 1285.716
DEMetro_Z 15 21.057 1.25e-14 1504.518
DEMetro_Z 18 30.043 1.75e-17 768.712
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -19.556 4.79e-14 -4.373
Metro_vs_DEMetro_Z 1 -23.389 1.82e-15 -5.230
Metro_vs_DEMetro_Z 2 -32.408 4.29e-18 -7.247
Metro_vs_DEMetro_Z 3 -25.414 3.93e-16 -5.683
Metro_vs_DEMetro_Z 4 -18.521 1.28e-13 -4.141
Metro_vs_DEMetro_Z 5 -25.636 3.35e-16 -5.732
DEMetro_Z_vs_SMC 0 19.633 4.46e-14 4.390
DEMetro_Z_vs_SMC 1 23.894 1.23e-15 5.343
DEMetro_Z_vs_SMC 2 32.454 4.18e-18 7.257
DEMetro_Z_vs_SMC 3 28.724 4.06e-17 6.423
DEMetro_Z_vs_SMC 4 21.019 1.29e-14 4.700
DEMetro_Z_vs_SMC 5 30.106 1.69e-17 6.732
HMC_vs_DEMetro_Z 0 -19.619 4.52e-14 -4.387
HMC_vs_DEMetro_Z 1 -22.312 4.32e-15 -4.989
HMC_vs_DEMetro_Z 2 -30.065 1.74e-17 -6.723
HMC_vs_DEMetro_Z 3 -25.952 2.67e-16 -5.803
HMC_vs_DEMetro_Z 4 -18.520 1.28e-13 -4.141
HMC_vs_DEMetro_Z 5 -25.710 3.17e-16 -5.749
HMC_vs_Metro 0 -4.746 0.000141 -1.061
HMC_vs_Metro 1 4.964 8.62e-05 1.110
HMC_vs_Metro 2 7.946 1.85e-07 1.777
HMC_vs_Metro 3 2.546 0.0197 0.569
HMC_vs_Metro 4 -0.408 0.688 -0.091
HMC_vs_Metro 5 0.102 0.919 0.023
HMC_vs_SMC 0 2.784 0.0118 0.623
HMC_vs_SMC 1 7.468 4.58e-07 1.670
HMC_vs_SMC 2 129.656 1.81e-29 28.992
HMC_vs_SMC 3 108.733 5.1e-28 24.313
HMC_vs_SMC 4 73.350 8.88e-25 16.402
HMC_vs_SMC 5 90.006 1.84e-26 20.126
Metro_vs_SMC 0 7.927 1.92e-07 1.772
Metro_vs_SMC 1 5.149 5.71e-05 1.151
Metro_vs_SMC 2 4.966 8.57e-05 1.110
Metro_vs_SMC 3 16.757 7.73e-13 3.747
Metro_vs_SMC 4 111.704 3.06e-28 24.978
Metro_vs_SMC 5 81.382 1.24e-25 18.198
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.036 0.031 0.002 2.802
HMC 8 0.391 0.035 0.005 72.986
HMC 10 0.747 0.036 0.005 140.526
HMC 12 0.894 0.040 0.007 120.570
HMC 15 1.100 0.040 0.006 172.027
HMC 18 1.330 0.044 0.012 106.989
SMC 5 0.032 0.031 0.002 0.319
SMC 8 0.033 0.035 0.005 -0.392
SMC 10 0.038 0.036 0.005 0.331
SMC 12 0.036 0.040 0.007 -0.484
SMC 15 0.043 0.040 0.006 0.463
SMC 18 0.049 0.044 0.012 0.425
Metro 5 0.049 0.031 0.002 10.394
Metro 8 0.142 0.035 0.005 21.891
Metro 10 0.304 0.036 0.005 52.868
Metro 12 0.783 0.040 0.007 105.001
Metro 15 1.106 0.040 0.006 172.976
Metro 18 1.328 0.044 0.012 106.810
DEMetro_Z 5 8.865 0.031 0.002 4983.352
DEMetro_Z 8 8.374 0.035 0.005 1706.816
DEMetro_Z 10 10.083 0.036 0.005 1986.233
DEMetro_Z 12 9.148 0.040 0.007 1285.716
DEMetro_Z 15 9.314 0.040 0.006 1504.518
DEMetro_Z 18 9.282 0.044 0.012 768.712
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.422 0.00246 2.884
HMC 8 7.806 2.39e-07 69.128
HMC 10 111.252 5.21e-30 127.106
HMC 12 127.701 2.52e-32 117.169
HMC 15 139.229 6.37e-32 162.480
HMC 18 131.076 2.83e-33 108.726
SMC 5 1.595 0.119 0.570
SMC 8 -1.454 0.154 -0.438
SMC 10 0.945 0.351 0.320
SMC 12 -1.840 0.0736 -0.559
SMC 15 1.038 0.307 0.422
SMC 18 0.983 0.333 0.408
Metro 5 8.308 5.76e-08 10.170
Metro 8 5.333 3.72e-05 21.137
Metro 10 4.870 0.000106 48.566
Metro 12 16.994 5.72e-13 102.950
Metro 15 159.644 8.63e-34 161.975
Metro 18 124.729 1.88e-32 108.563
DEMetro_Z 5 88.072 2.57e-26 697.737
DEMetro_Z 8 68.305 2.74e-24 302.495
DEMetro_Z 10 97.716 2.2e-27 291.298
DEMetro_Z 12 53.518 2.88e-22 247.951
DEMetro_Z 15 68.061 2.92e-24 296.984
DEMetro_Z 18 77.531 1.42e-25 187.566
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 87.345 3.25e-26 19.531
DEMetro_Z_vs_SMC 1 68.546 3.2e-24 15.327
DEMetro_Z_vs_SMC 2 98.352 3.42e-27 21.992
DEMetro_Z_vs_SMC 3 53.936 2.98e-22 12.061
DEMetro_Z_vs_SMC 4 67.227 4.63e-24 15.033
DEMetro_Z_vs_SMC 5 79.725 1.83e-25 17.827
HMC_vs_Metro 0 -4.679 0.000164 -1.046
HMC_vs_Metro 1 5.288 4.2e-05 1.182
HMC_vs_Metro 2 8.099 1.4e-07 1.811
HMC_vs_Metro 3 2.343 0.0301 0.524
HMC_vs_Metro 4 0.517 0.611 0.116
HMC_vs_Metro 5 0.192 0.85 0.043
Metro_vs_DEMetro_Z 0 -81.076 1.33e-25 -18.129
Metro_vs_DEMetro_Z 1 -48.690 2.05e-21 -10.887
Metro_vs_DEMetro_Z 2 -25.309 4.24e-16 -5.659
Metro_vs_DEMetro_Z 3 -17.962 2.23e-13 -4.016
Metro_vs_DEMetro_Z 4 -31.605 6.85e-18 -7.067
Metro_vs_DEMetro_Z 5 -27.617 8.43e-17 -6.175
HMC_vs_SMC 0 2.625 0.0167 0.587
HMC_vs_SMC 1 7.854 2.2e-07 1.756
HMC_vs_SMC 2 112.733 2.57e-28 25.208
HMC_vs_SMC 3 139.649 4.42e-30 31.227
HMC_vs_SMC 4 142.443 3.03e-30 31.851
HMC_vs_SMC 5 112.882 2.51e-28 25.241
Metro_vs_SMC 0 7.980 1.74e-07 1.784
Metro_vs_SMC 1 5.449 2.95e-05 1.218
Metro_vs_SMC 2 4.843 0.000113 1.083
Metro_vs_SMC 3 17.219 4.75e-13 3.850
Metro_vs_SMC 4 143.876 2.51e-30 32.172
Metro_vs_SMC 5 115.141 1.72e-28 25.746
HMC_vs_DEMetro_Z 0 -85.040 5.39e-26 -19.016
HMC_vs_DEMetro_Z 1 -23.838 1.28e-15 -5.330
HMC_vs_DEMetro_Z 2 -61.813 2.26e-23 -13.822
HMC_vs_DEMetro_Z 3 -27.424 9.61e-17 -6.132
HMC_vs_DEMetro_Z 4 -33.739 2.02e-18 -7.544
HMC_vs_DEMetro_Z 5 -27.492 9.17e-17 -6.147
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.017 0.013 0.001 2.884
HMC 8 0.220 0.014 0.003 69.128
HMC 10 0.408 0.014 0.003 127.106
HMC 12 0.457 0.015 0.004 117.169
HMC 15 0.512 0.012 0.003 162.480
HMC 18 0.543 0.013 0.005 108.726
SMC 5 0.014 0.013 0.001 0.570
SMC 8 0.013 0.014 0.003 -0.438
SMC 10 0.015 0.014 0.003 0.320
SMC 12 0.013 0.015 0.004 -0.559
SMC 15 0.014 0.012 0.003 0.422
SMC 18 0.015 0.013 0.005 0.408
Metro 5 0.027 0.013 0.001 10.170
Metro 8 0.077 0.014 0.003 21.137
Metro 10 0.164 0.014 0.003 48.566
Metro 12 0.403 0.015 0.004 102.950
Metro 15 0.510 0.012 0.003 161.975
Metro 18 0.542 0.013 0.005 108.563
DEMetro_Z 5 0.921 0.013 0.001 697.737
DEMetro_Z 8 0.915 0.014 0.003 302.495
DEMetro_Z 10 0.916 0.014 0.003 291.298
DEMetro_Z 12 0.951 0.015 0.004 247.951
DEMetro_Z 15 0.925 0.012 0.003 296.984
DEMetro_Z 18 0.927 0.013 0.005 187.566
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
Trace Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Varying_Mode_Distance_with_high_Correlation (Mixture, mm, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.189 5.19e-05 38.891
HMC 8 4.199 0.000484 26.345
HMC 10 3.628 0.00178 17.931
HMC 12 4.425 0.000286 17.304
HMC 15 5.066 6.84e-05 43.335
HMC 18 6.006 8.72e-06 29.855
SMC 5 0.479 0.635 0.169
SMC 8 1.316 0.197 0.485
SMC 10 0.772 0.445 0.221
SMC 12 -0.229 0.82 -0.065
SMC 15 1.510 0.142 0.766
SMC 18 -0.057 0.955 -0.017
Metro 5 6.916 1.3e-06 24.693
Metro 8 5.663 1.83e-05 29.591
Metro 10 4.332 0.000358 27.294
Metro 12 5.245 4.47e-05 17.042
Metro 15 4.761 0.000136 41.259
Metro 18 6.819 1.61e-06 31.659
DEMetro_Z 5 5.787 1.4e-05 30.721
DEMetro_Z 8 7.917 1.89e-07 36.514
DEMetro_Z 10 5.275 4.25e-05 23.689
DEMetro_Z 12 5.050 7.01e-05 23.056
DEMetro_Z 15 7.869 2.12e-07 65.297
DEMetro_Z 18 8.861 3.38e-08 35.355
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.840 0.411 0.188
HMC_vs_DEMetro_Z 1 -1.368 0.187 -0.306
HMC_vs_DEMetro_Z 2 -0.960 0.349 -0.215
HMC_vs_DEMetro_Z 3 -0.974 0.342 -0.218
HMC_vs_DEMetro_Z 4 -1.813 0.0857 -0.405
HMC_vs_DEMetro_Z 5 -0.782 0.444 -0.175
Metro_vs_SMC 0 6.741 1.93e-06 1.507
Metro_vs_SMC 1 5.622 2.02e-05 1.257
Metro_vs_SMC 2 4.291 0.000394 0.959
Metro_vs_SMC 3 5.281 4.26e-05 1.181
Metro_vs_SMC 4 4.652 0.000174 1.040
Metro_vs_SMC 5 6.891 1.43e-06 1.541
Metro_vs_DEMetro_Z 0 -1.027 0.317 -0.230
Metro_vs_DEMetro_Z 1 -1.206 0.243 -0.270
Metro_vs_DEMetro_Z 2 0.505 0.62 0.113
Metro_vs_DEMetro_Z 3 -1.104 0.283 -0.247
Metro_vs_DEMetro_Z 4 -2.101 0.0492 -0.470
Metro_vs_DEMetro_Z 5 -0.619 0.543 -0.138
HMC_vs_Metro 0 2.220 0.0388 0.496
HMC_vs_Metro 1 -0.465 0.647 -0.104
HMC_vs_Metro 2 -1.640 0.118 -0.367
HMC_vs_Metro 3 0.063 0.951 0.014
HMC_vs_Metro 4 0.225 0.825 0.050
HMC_vs_Metro 5 -0.411 0.685 -0.092
HMC_vs_SMC 0 5.168 5.47e-05 1.156
HMC_vs_SMC 1 4.198 0.000487 0.939
HMC_vs_SMC 2 3.601 0.0019 0.805
HMC_vs_SMC 3 4.502 0.000244 1.007
HMC_vs_SMC 4 4.937 9.14e-05 1.104
HMC_vs_SMC 5 6.164 6.35e-06 1.378
DEMetro_Z_vs_SMC 0 5.863 1.2e-05 1.311
DEMetro_Z_vs_SMC 1 7.851 2.21e-07 1.755
DEMetro_Z_vs_SMC 2 5.261 4.45e-05 1.176
DEMetro_Z_vs_SMC 3 5.091 6.5e-05 1.138
DEMetro_Z_vs_SMC 4 7.600 3.56e-07 1.699
DEMetro_Z_vs_SMC 5 8.700 4.72e-08 1.945
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.771 0.034 0.019 38.891
HMC 8 0.925 0.047 0.033 26.345
HMC 10 0.903 0.048 0.048 17.931
HMC 12 1.305 0.088 0.070 17.304
HMC 15 2.163 0.073 0.048 43.335
HMC 18 3.034 0.135 0.097 29.855
SMC 5 0.038 0.034 0.019 0.169
SMC 8 0.063 0.047 0.033 0.485
SMC 10 0.059 0.048 0.048 0.221
SMC 12 0.083 0.088 0.070 -0.065
SMC 15 0.110 0.073 0.048 0.766
SMC 18 0.133 0.135 0.097 -0.017
Metro 5 0.502 0.034 0.019 24.693
Metro 8 1.033 0.047 0.033 29.591
Metro 10 1.349 0.048 0.048 27.294
Metro 12 1.287 0.088 0.070 17.042
Metro 15 2.063 0.073 0.048 41.259
Metro 18 3.209 0.135 0.097 31.659
DEMetro_Z 5 0.617 0.034 0.019 30.721
DEMetro_Z 8 1.264 0.047 0.033 36.514
DEMetro_Z 10 1.178 0.048 0.048 23.689
DEMetro_Z 12 1.710 0.088 0.070 23.056
DEMetro_Z 15 3.223 0.073 0.048 65.297
DEMetro_Z 18 3.568 0.135 0.097 35.355
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.925 0.000906 30.207
HMC 8 3.220 0.00451 29.367
HMC 10 2.876 0.00968 30.943
HMC 12 3.430 0.00281 47.628
HMC 15 3.709 0.00149 75.362
HMC 18 4.215 0.000469 125.265
SMC 5 -1.089 0.283 -0.343
SMC 8 1.176 0.247 0.396
SMC 10 0.712 0.481 0.273
SMC 12 1.113 0.273 0.420
SMC 15 -0.832 0.411 -0.255
SMC 18 1.509 0.14 0.555
Metro 5 4.922 9.05e-05 12.179
Metro 8 4.354 0.00034 28.872
Metro 10 3.600 0.00191 61.617
Metro 12 6.271 5.02e-06 43.962
Metro 15 3.630 0.00178 74.158
Metro 18 4.529 0.00023 130.892
DEMetro_Z 5 3.409 0.00293 19.450
DEMetro_Z 8 4.206 0.000477 35.230
DEMetro_Z 10 3.702 0.00151 39.092
DEMetro_Z 12 3.732 0.00141 75.489
DEMetro_Z 15 5.283 4.24e-05 130.227
DEMetro_Z 18 5.135 5.88e-05 141.210
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.983 0.000796 0.891
HMC_vs_SMC 1 3.179 0.00494 0.711
HMC_vs_SMC 2 2.838 0.0105 0.635
HMC_vs_SMC 3 3.408 0.00295 0.762
HMC_vs_SMC 4 3.712 0.00148 0.830
HMC_vs_SMC 5 4.192 0.000495 0.937
Metro_vs_DEMetro_Z 0 -1.207 0.242 -0.270
Metro_vs_DEMetro_Z 1 -0.620 0.543 -0.139
Metro_vs_DEMetro_Z 2 1.173 0.255 0.262
Metro_vs_DEMetro_Z 3 -1.522 0.144 -0.340
Metro_vs_DEMetro_Z 4 -1.983 0.062 -0.443
Metro_vs_DEMetro_Z 5 -0.305 0.764 -0.068
HMC_vs_Metro 0 2.513 0.0212 0.562
HMC_vs_Metro 1 0.068 0.946 0.015
HMC_vs_Metro 2 -2.075 0.0518 -0.464
HMC_vs_Metro 3 0.264 0.794 0.059
HMC_vs_Metro 4 0.051 0.96 0.011
HMC_vs_Metro 5 -0.188 0.853 -0.042
HMC_vs_DEMetro_Z 0 1.088 0.29 0.243
HMC_vs_DEMetro_Z 1 -0.471 0.643 -0.105
HMC_vs_DEMetro_Z 2 -0.591 0.562 -0.132
HMC_vs_DEMetro_Z 3 -1.144 0.267 -0.256
HMC_vs_DEMetro_Z 4 -1.584 0.13 -0.354
HMC_vs_DEMetro_Z 5 -0.383 0.706 -0.086
Metro_vs_SMC 0 4.978 8.35e-05 1.113
Metro_vs_SMC 1 4.282 0.000403 0.957
Metro_vs_SMC 2 3.590 0.00195 0.803
Metro_vs_SMC 3 6.143 6.63e-06 1.374
Metro_vs_SMC 4 3.625 0.0018 0.810
Metro_vs_SMC 5 4.498 0.000246 1.006
DEMetro_Z_vs_SMC 0 3.466 0.00258 0.775
DEMetro_Z_vs_SMC 1 4.147 0.000548 0.927
DEMetro_Z_vs_SMC 2 3.632 0.00178 0.812
DEMetro_Z_vs_SMC 3 3.696 0.00153 0.826
DEMetro_Z_vs_SMC 4 5.281 4.26e-05 1.181
DEMetro_Z_vs_SMC 5 5.094 6.45e-05 1.139
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 1.375 0.077 0.043 30.207
HMC 8 2.451 0.089 0.080 29.367
HMC 10 2.759 0.120 0.085 30.943
HMC 12 4.558 0.141 0.093 47.628
HMC 15 11.123 0.205 0.145 75.362
HMC 18 19.326 0.184 0.153 125.265
SMC 5 0.062 0.077 0.043 -0.343
SMC 8 0.120 0.089 0.080 0.396
SMC 10 0.143 0.120 0.085 0.273
SMC 12 0.180 0.141 0.093 0.420
SMC 15 0.168 0.205 0.145 -0.255
SMC 18 0.269 0.184 0.153 0.555
Metro 5 0.601 0.077 0.043 12.179
Metro 8 2.412 0.089 0.080 28.872
Metro 10 5.375 0.120 0.085 61.617
Metro 12 4.218 0.141 0.093 43.962
Metro 15 10.949 0.205 0.145 74.158
Metro 18 20.186 0.184 0.153 130.892
DEMetro_Z 5 0.913 0.077 0.043 19.450
DEMetro_Z 8 2.923 0.089 0.080 35.230
DEMetro_Z 10 3.454 0.120 0.085 39.092
DEMetro_Z 12 7.141 0.141 0.093 75.489
DEMetro_Z 15 19.072 0.205 0.145 130.227
DEMetro_Z 18 21.762 0.184 0.153 141.210
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.087 6.52e-05 39.879
HMC 8 4.128 0.00057 31.457
HMC 10 3.622 0.00181 20.024
HMC 12 4.333 0.000355 18.108
HMC 15 5.038 7.28e-05 48.006
HMC 18 5.936 1.01e-05 31.268
SMC 5 -0.392 0.697 -0.129
SMC 8 1.856 0.0721 0.709
SMC 10 0.567 0.574 0.162
SMC 12 -0.168 0.868 -0.048
SMC 15 1.509 0.143 0.798
SMC 18 0.348 0.729 0.105
Metro 5 7.478 4.27e-07 26.519
Metro 8 5.758 1.49e-05 35.985
Metro 10 4.395 0.00031 31.281
Metro 12 5.534 2.38e-05 20.088
Metro 15 4.891 0.000101 48.320
Metro 18 7.075 9.61e-07 32.232
DEMetro_Z 5 6.191 5.9e-06 31.648
DEMetro_Z 8 7.524 4.03e-07 43.266
DEMetro_Z 10 5.473 2.75e-05 26.226
DEMetro_Z 12 5.085 6.5e-05 24.933
DEMetro_Z 15 7.545 3.93e-07 76.398
DEMetro_Z 18 8.963 2.84e-08 36.963
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.892 0.384 -0.199
Metro_vs_DEMetro_Z 1 -1.056 0.304 -0.236
Metro_vs_DEMetro_Z 2 0.628 0.538 0.140
Metro_vs_DEMetro_Z 3 -0.810 0.428 -0.181
Metro_vs_DEMetro_Z 4 -2.138 0.0457 -0.478
Metro_vs_DEMetro_Z 5 -0.770 0.451 -0.172
DEMetro_Z_vs_SMC 0 6.277 5.02e-06 1.403
DEMetro_Z_vs_SMC 1 7.373 5.51e-07 1.649
DEMetro_Z_vs_SMC 2 5.466 2.84e-05 1.222
DEMetro_Z_vs_SMC 3 5.098 6.39e-05 1.140
DEMetro_Z_vs_SMC 4 7.313 6.19e-07 1.635
DEMetro_Z_vs_SMC 5 8.747 4.35e-08 1.956
HMC_vs_DEMetro_Z 0 0.836 0.414 0.187
HMC_vs_DEMetro_Z 1 -1.261 0.223 -0.282
HMC_vs_DEMetro_Z 2 -0.930 0.364 -0.208
HMC_vs_DEMetro_Z 3 -1.104 0.284 -0.247
HMC_vs_DEMetro_Z 4 -2.011 0.0588 -0.450
HMC_vs_DEMetro_Z 5 -0.768 0.452 -0.172
HMC_vs_Metro 0 1.888 0.0744 0.422
HMC_vs_Metro 1 -0.523 0.607 -0.117
HMC_vs_Metro 2 -1.769 0.093 -0.395
HMC_vs_Metro 3 -0.424 0.676 -0.095
HMC_vs_Metro 4 -0.029 0.977 -0.007
HMC_vs_Metro 5 -0.205 0.84 -0.046
HMC_vs_SMC 0 5.117 6.12e-05 1.144
HMC_vs_SMC 1 4.101 0.000609 0.917
HMC_vs_SMC 2 3.602 0.0019 0.805
HMC_vs_SMC 3 4.392 0.000313 0.982
HMC_vs_SMC 4 4.923 9.45e-05 1.101
HMC_vs_SMC 5 6.056 7.98e-06 1.354
Metro_vs_SMC 0 7.408 5.15e-07 1.656
Metro_vs_SMC 1 5.685 1.76e-05 1.271
Metro_vs_SMC 2 4.363 0.000335 0.976
Metro_vs_SMC 3 5.554 2.34e-05 1.242
Metro_vs_SMC 4 4.779 0.00013 1.069
Metro_vs_SMC 5 7.122 9.01e-07 1.592
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.692 0.049 0.016 39.879
HMC 8 0.831 0.058 0.025 31.457
HMC 10 0.840 0.063 0.039 20.024
HMC 12 1.134 0.095 0.057 18.108
HMC 15 1.904 0.084 0.038 48.006
HMC 18 2.767 0.133 0.084 31.268
SMC 5 0.047 0.049 0.016 -0.129
SMC 8 0.076 0.058 0.025 0.709
SMC 10 0.070 0.063 0.039 0.162
SMC 12 0.092 0.095 0.057 -0.048
SMC 15 0.114 0.084 0.038 0.798
SMC 18 0.142 0.133 0.084 0.105
Metro 5 0.476 0.049 0.016 26.519
Metro 8 0.942 0.058 0.025 35.985
Metro 10 1.277 0.063 0.039 31.281
Metro 12 1.248 0.095 0.057 20.088
Metro 15 1.916 0.084 0.038 48.320
Metro 18 2.848 0.133 0.084 32.232
DEMetro_Z 5 0.559 0.049 0.016 31.648
DEMetro_Z 8 1.121 0.058 0.025 43.266
DEMetro_Z 10 1.081 0.063 0.039 26.226
DEMetro_Z 12 1.526 0.095 0.057 24.933
DEMetro_Z 15 2.981 0.084 0.038 76.398
DEMetro_Z 18 3.247 0.133 0.084 36.963
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.041 7.23e-05 43.654
HMC 8 4.230 0.000452 32.861
HMC 10 3.712 0.00147 21.424
HMC 12 4.479 0.000254 20.116
HMC 15 5.215 4.91e-05 45.586
HMC 18 6.277 4.95e-06 36.487
SMC 5 -0.384 0.703 -0.137
SMC 8 1.575 0.124 0.585
SMC 10 0.786 0.437 0.229
SMC 12 -0.152 0.88 -0.044
SMC 15 1.362 0.183 0.622
SMC 18 0.349 0.729 0.112
Metro 5 7.089 9.27e-07 27.735
Metro 8 5.614 2.04e-05 36.493
Metro 10 4.447 0.000276 32.741
Metro 12 5.404 3.18e-05 20.463
Metro 15 4.854 0.00011 43.570
Metro 18 7.177 7.93e-07 39.377
DEMetro_Z 5 5.591 2.14e-05 34.298
DEMetro_Z 8 7.688 2.95e-07 45.296
DEMetro_Z 10 5.332 3.77e-05 28.633
DEMetro_Z 12 5.174 5.34e-05 26.789
DEMetro_Z 15 8.121 1.33e-07 68.385
DEMetro_Z 18 9.360 1.45e-08 43.251
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.679 1.79e-05 1.270
DEMetro_Z_vs_SMC 1 7.598 3.57e-07 1.699
DEMetro_Z_vs_SMC 2 5.315 3.95e-05 1.188
DEMetro_Z_vs_SMC 3 5.191 5.19e-05 1.161
DEMetro_Z_vs_SMC 4 7.898 2.03e-07 1.766
DEMetro_Z_vs_SMC 5 9.181 2.05e-08 2.053
HMC_vs_Metro 0 2.145 0.0451 0.480
HMC_vs_Metro 1 -0.427 0.674 -0.095
HMC_vs_Metro 2 -1.660 0.113 -0.371
HMC_vs_Metro 3 -0.070 0.945 -0.016
HMC_vs_Metro 4 0.216 0.832 0.048
HMC_vs_Metro 5 -0.564 0.579 -0.126
Metro_vs_DEMetro_Z 0 -0.993 0.333 -0.222
Metro_vs_DEMetro_Z 1 -1.227 0.235 -0.274
Metro_vs_DEMetro_Z 2 0.483 0.634 0.108
Metro_vs_DEMetro_Z 3 -1.001 0.329 -0.224
Metro_vs_DEMetro_Z 4 -2.109 0.0485 -0.472
Metro_vs_DEMetro_Z 5 -0.541 0.595 -0.121
HMC_vs_SMC 0 5.059 6.96e-05 1.131
HMC_vs_SMC 1 4.212 0.000472 0.942
HMC_vs_SMC 2 3.690 0.00156 0.825
HMC_vs_SMC 3 4.529 0.00023 1.013
HMC_vs_SMC 4 5.091 6.49e-05 1.138
HMC_vs_SMC 5 6.384 4.01e-06 1.428
Metro_vs_SMC 0 7.005 1.14e-06 1.566
Metro_vs_SMC 1 5.546 2.39e-05 1.240
Metro_vs_SMC 2 4.407 0.000303 0.985
Metro_vs_SMC 3 5.414 3.18e-05 1.211
Metro_vs_SMC 4 4.755 0.000138 1.063
Metro_vs_SMC 5 7.184 7.97e-07 1.606
HMC_vs_DEMetro_Z 0 0.839 0.412 0.188
HMC_vs_DEMetro_Z 1 -1.331 0.199 -0.298
HMC_vs_DEMetro_Z 2 -1.009 0.326 -0.226
HMC_vs_DEMetro_Z 3 -0.978 0.34 -0.219
HMC_vs_DEMetro_Z 4 -1.850 0.08 -0.414
HMC_vs_DEMetro_Z 5 -0.822 0.421 -0.184
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.231 0.012 0.005 43.654
HMC 8 0.205 0.010 0.006 32.861
HMC 10 0.165 0.009 0.007 21.424
HMC 12 0.202 0.013 0.009 20.116
HMC 15 0.264 0.008 0.006 45.586
HMC 18 0.309 0.012 0.008 36.487
SMC 5 0.012 0.012 0.005 -0.137
SMC 8 0.014 0.010 0.006 0.585
SMC 10 0.010 0.009 0.007 0.229
SMC 12 0.012 0.013 0.009 -0.044
SMC 15 0.012 0.008 0.006 0.622
SMC 18 0.012 0.012 0.008 0.112
Metro 5 0.151 0.012 0.005 27.735
Metro 8 0.226 0.010 0.006 36.493
Metro 10 0.247 0.009 0.007 32.741
Metro 12 0.205 0.013 0.009 20.463
Metro 15 0.253 0.008 0.006 43.570
Metro 18 0.333 0.012 0.008 39.377
DEMetro_Z 5 0.184 0.012 0.005 34.298
DEMetro_Z 8 0.278 0.010 0.006 45.296
DEMetro_Z 10 0.217 0.009 0.007 28.633
DEMetro_Z 12 0.264 0.013 0.009 26.789
DEMetro_Z 15 0.392 0.008 0.006 68.385
DEMetro_Z 18 0.364 0.012 0.008 43.251
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 178.260 1.25e-43 91.337
HMC 8 210.921 5.18e-54 83.569
HMC 10 205.637 2.17e-57 73.168
HMC 12 194.815 2.7e-58 59.248
HMC 15 226.819 1.26e-48 107.934
HMC 18 236.657 1.04e-55 64.118
SMC 5 0.102 0.92 0.040
SMC 8 1.318 0.196 0.451
SMC 10 1.914 0.0632 0.619
SMC 12 -0.395 0.695 -0.114
SMC 15 1.474 0.151 0.683
SMC 18 -1.340 0.189 -0.371
Metro 5 5.619 2.02e-05 34.774
Metro 8 149.220 1.27e-39 83.532
Metro 10 197.561 1.95e-55 73.218
Metro 12 162.410 5.1e-53 59.068
Metro 15 177.659 3.77e-40 107.276
Metro 18 218.978 2.7e-59 64.339
DEMetro_Z 5 6.965 1.22e-06 64.809
DEMetro_Z 8 21.213 9.34e-15 79.867
DEMetro_Z 10 199.277 1.13e-55 73.628
DEMetro_Z 12 184.949 1.04e-57 59.437
DEMetro_Z 15 213.374 4.43e-46 108.064
DEMetro_Z 18 230.810 2.09e-57 64.299
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 2.783 0.0119 0.622
HMC_vs_DEMetro_Z 1 0.962 0.348 0.215
HMC_vs_DEMetro_Z 2 -1.501 0.15 -0.336
HMC_vs_DEMetro_Z 3 -0.715 0.483 -0.160
HMC_vs_DEMetro_Z 4 -0.190 0.851 -0.043
HMC_vs_DEMetro_Z 5 -0.894 0.383 -0.200
Metro_vs_SMC 0 5.612 2.07e-05 1.255
Metro_vs_SMC 1 138.837 4.94e-30 31.045
Metro_vs_SMC 2 181.660 3e-32 40.620
Metro_vs_SMC 3 173.223 7.4e-32 38.734
Metro_vs_SMC 4 122.341 5.45e-29 27.356
Metro_vs_SMC 5 223.756 5.73e-34 50.033
Metro_vs_DEMetro_Z 0 -2.282 0.0342 -0.510
Metro_vs_DEMetro_Z 1 0.964 0.347 0.216
Metro_vs_DEMetro_Z 2 -0.857 0.402 -0.192
Metro_vs_DEMetro_Z 3 -1.070 0.298 -0.239
Metro_vs_DEMetro_Z 4 -1.132 0.272 -0.253
Metro_vs_DEMetro_Z 5 0.171 0.866 0.038
HMC_vs_Metro 0 9.058 2.53e-08 2.025
HMC_vs_Metro 1 0.083 0.934 0.019
HMC_vs_Metro 2 -0.106 0.917 -0.024
HMC_vs_Metro 3 0.752 0.461 0.168
HMC_vs_Metro 4 1.549 0.138 0.346
HMC_vs_Metro 5 -1.966 0.0641 -0.440
HMC_vs_SMC 0 144.952 2.18e-30 32.412
HMC_vs_SMC 1 184.816 2.16e-32 41.326
HMC_vs_SMC 2 198.648 5.49e-33 44.419
HMC_vs_SMC 3 195.639 7.34e-33 43.746
HMC_vs_SMC 4 149.500 1.21e-30 33.429
HMC_vs_SMC 5 243.743 1.13e-34 54.503
DEMetro_Z_vs_SMC 0 6.926 1.33e-06 1.549
DEMetro_Z_vs_SMC 1 21.392 9.34e-15 4.783
DEMetro_Z_vs_SMC 2 307.755 1.34e-36 68.816
DEMetro_Z_vs_SMC 3 188.560 1.48e-32 42.163
DEMetro_Z_vs_SMC 4 170.632 9.85e-32 38.155
DEMetro_Z_vs_SMC 5 249.059 7.48e-35 55.691
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 1.765 0.034 0.019 91.337
HMC 8 2.832 0.047 0.033 83.569
HMC 10 3.536 0.048 0.048 73.168
HMC 12 4.255 0.088 0.070 59.248
HMC 15 5.280 0.073 0.048 107.934
HMC 18 6.361 0.135 0.097 64.118
SMC 5 0.035 0.034 0.019 0.040
SMC 8 0.062 0.047 0.033 0.451
SMC 10 0.078 0.048 0.048 0.619
SMC 12 0.080 0.088 0.070 -0.114
SMC 15 0.106 0.073 0.048 0.683
SMC 18 0.099 0.135 0.097 -0.371
Metro 5 0.693 0.034 0.019 34.774
Metro 8 2.831 0.047 0.033 83.532
Metro 10 3.538 0.048 0.048 73.218
Metro 12 4.243 0.088 0.070 59.068
Metro 15 5.248 0.073 0.048 107.276
Metro 18 6.382 0.135 0.097 64.339
DEMetro_Z 5 1.262 0.034 0.019 64.809
DEMetro_Z 8 2.709 0.047 0.033 79.867
DEMetro_Z 10 3.558 0.048 0.048 73.628
DEMetro_Z 12 4.269 0.088 0.070 59.437
DEMetro_Z 15 5.286 0.073 0.048 108.064
DEMetro_Z 18 6.378 0.135 0.097 64.299
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 207.553 8.5e-47 101.201
HMC 8 334.946 1.13e-58 139.403
HMC 10 536.571 4.36e-69 206.210
HMC 12 655.129 4.86e-68 272.803
HMC 15 739.594 6.69e-76 273.069
HMC 18 1020.837 2.43e-81 373.472
SMC 5 -0.299 0.766 -0.099
SMC 8 1.251 0.219 0.434
SMC 10 0.202 0.841 0.070
SMC 12 1.201 0.237 0.421
SMC 15 -1.083 0.288 -0.273
SMC 18 0.690 0.495 0.243
Metro 5 3.805 0.00119 25.706
Metro 8 363.515 2.32e-63 139.405
Metro 10 522.171 2.12e-67 206.141
Metro 12 550.654 2.93e-58 272.822
Metro 15 732.732 2.68e-75 273.078
Metro 18 957.046 7.27e-77 373.686
DEMetro_Z 5 6.657 2.28e-06 71.116
DEMetro_Z 8 19.581 4.48e-14 132.904
DEMetro_Z 10 577.690 1.25e-73 205.957
DEMetro_Z 12 638.499 1.95e-66 272.774
DEMetro_Z 15 718.064 5.72e-74 273.116
DEMetro_Z 18 1003.685 3.45e-80 373.520
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 238.979 1.64e-34 53.437
HMC_vs_SMC 1 278.204 9.14e-36 62.208
HMC_vs_SMC 2 702.257 2.1e-43 157.029
HMC_vs_SMC 3 566.820 1.23e-41 126.745
HMC_vs_SMC 4 834.229 7.95e-45 186.539
HMC_vs_SMC 5 809.861 1.4e-44 181.090
Metro_vs_DEMetro_Z 0 -2.972 0.00783 -0.665
Metro_vs_DEMetro_Z 1 0.956 0.351 0.214
Metro_vs_DEMetro_Z 2 0.875 0.392 0.196
Metro_vs_DEMetro_Z 3 0.230 0.82 0.051
Metro_vs_DEMetro_Z 4 -0.347 0.733 -0.077
Metro_vs_DEMetro_Z 5 1.351 0.193 0.302
HMC_vs_Metro 0 11.156 8.79e-10 2.495
HMC_vs_Metro 1 -0.008 0.994 -0.002
HMC_vs_Metro 2 0.313 0.758 0.070
HMC_vs_Metro 3 -0.103 0.919 -0.023
HMC_vs_Metro 4 -0.075 0.941 -0.017
HMC_vs_Metro 5 -2.295 0.0333 -0.513
HMC_vs_DEMetro_Z 0 2.812 0.0111 0.629
HMC_vs_DEMetro_Z 1 0.961 0.349 0.215
HMC_vs_DEMetro_Z 2 2.090 0.0503 0.467
HMC_vs_DEMetro_Z 3 0.217 0.83 0.049
HMC_vs_DEMetro_Z 4 -0.525 0.606 -0.117
HMC_vs_DEMetro_Z 5 -0.612 0.548 -0.137
Metro_vs_SMC 0 3.801 0.00121 0.850
Metro_vs_SMC 1 316.075 8.1e-37 70.676
Metro_vs_SMC 2 572.223 1.03e-41 127.953
Metro_vs_SMC 3 451.901 9.1e-40 101.048
Metro_vs_SMC 4 799.753 1.77e-44 178.830
Metro_vs_SMC 5 801.471 1.7e-44 179.214
DEMetro_Z_vs_SMC 0 6.695 2.12e-06 1.497
DEMetro_Z_vs_SMC 1 19.718 4.12e-14 4.409
DEMetro_Z_vs_SMC 2 691.958 2.78e-43 154.727
DEMetro_Z_vs_SMC 3 554.422 1.87e-41 123.972
DEMetro_Z_vs_SMC 4 820.678 1.09e-44 183.509
DEMetro_Z_vs_SMC 5 802.535 1.66e-44 179.452
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 4.426 0.077 0.043 101.201
HMC 8 11.304 0.089 0.080 139.403
HMC 10 17.706 0.120 0.085 206.210
HMC 12 25.437 0.141 0.093 272.803
HMC 15 39.767 0.205 0.145 273.069
HMC 18 57.255 0.184 0.153 373.472
SMC 5 0.073 0.077 0.043 -0.099
SMC 8 0.124 0.089 0.080 0.434
SMC 10 0.126 0.120 0.085 0.070
SMC 12 0.180 0.141 0.093 0.421
SMC 15 0.165 0.205 0.145 -0.273
SMC 18 0.221 0.184 0.153 0.243
Metro 5 1.182 0.077 0.043 25.706
Metro 8 11.304 0.089 0.080 139.405
Metro 10 17.700 0.120 0.085 206.141
Metro 12 25.439 0.141 0.093 272.822
Metro 15 39.768 0.205 0.145 273.078
Metro 18 57.288 0.184 0.153 373.686
DEMetro_Z 5 3.133 0.077 0.043 71.116
DEMetro_Z 8 10.781 0.089 0.080 132.904
DEMetro_Z 10 17.684 0.120 0.085 205.957
DEMetro_Z 12 25.435 0.141 0.093 272.774
DEMetro_Z 15 39.774 0.205 0.145 273.116
DEMetro_Z 18 57.262 0.184 0.153 373.520
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 73.984 5.11e-26 96.576
HMC 8 62.169 4.08e-24 100.794
HMC 10 65.878 2.99e-25 78.048
HMC 12 62.523 3.76e-25 65.851
HMC 15 74.145 1.44e-25 124.496
HMC 18 72.843 2.85e-27 64.936
SMC 5 -0.335 0.74 -0.120
SMC 8 1.628 0.113 0.629
SMC 10 1.892 0.0662 0.589
SMC 12 -0.386 0.701 -0.110
SMC 15 1.346 0.189 0.655
SMC 18 -1.177 0.247 -0.322
Metro 5 5.770 1.45e-05 36.998
Metro 8 58.362 1.75e-23 101.736
Metro 10 54.459 4.15e-23 81.189
Metro 12 63.163 3.01e-25 66.437
Metro 15 77.969 3.98e-26 120.549
Metro 18 80.222 1.7e-28 67.660
DEMetro_Z 5 6.918 1.34e-06 68.636
DEMetro_Z 8 19.157 6.44e-14 97.835
DEMetro_Z 10 74.148 1.45e-26 80.746
DEMetro_Z 12 59.762 1.48e-24 66.804
DEMetro_Z 15 58.874 2.3e-23 125.255
DEMetro_Z 18 72.686 3.49e-27 65.641
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.310 0.0323 -0.517
Metro_vs_DEMetro_Z 1 0.691 0.498 0.155
Metro_vs_DEMetro_Z 2 0.220 0.828 0.049
Metro_vs_DEMetro_Z 3 -0.238 0.814 -0.053
Metro_vs_DEMetro_Z 4 -1.688 0.108 -0.377
Metro_vs_DEMetro_Z 5 2.311 0.0322 0.517
DEMetro_Z_vs_SMC 0 6.903 1.39e-06 1.544
DEMetro_Z_vs_SMC 1 19.337 5.87e-14 4.324
DEMetro_Z_vs_SMC 2 81.144 1.31e-25 18.144
DEMetro_Z_vs_SMC 3 60.199 3.74e-23 13.461
DEMetro_Z_vs_SMC 4 56.410 1.28e-22 12.614
DEMetro_Z_vs_SMC 5 71.027 1.63e-24 15.882
HMC_vs_DEMetro_Z 0 2.711 0.0139 0.606
HMC_vs_DEMetro_Z 1 0.523 0.607 0.117
HMC_vs_DEMetro_Z 2 -1.409 0.175 -0.315
HMC_vs_DEMetro_Z 3 -0.683 0.503 -0.153
HMC_vs_DEMetro_Z 4 -0.261 0.797 -0.058
HMC_vs_DEMetro_Z 5 -0.534 0.599 -0.119
HMC_vs_Metro 0 9.130 2.23e-08 2.042
HMC_vs_Metro 1 -0.357 0.725 -0.080
HMC_vs_Metro 2 -1.829 0.0831 -0.409
HMC_vs_Metro 3 -0.408 0.688 -0.091
HMC_vs_Metro 4 1.492 0.152 0.334
HMC_vs_Metro 5 -2.258 0.0359 -0.505
HMC_vs_SMC 0 73.184 9.27e-25 16.365
HMC_vs_SMC 1 62.535 1.82e-23 13.983
HMC_vs_SMC 2 61.458 2.52e-23 13.743
HMC_vs_SMC 3 63.424 1.39e-23 14.182
HMC_vs_SMC 4 67.882 3.85e-24 15.179
HMC_vs_SMC 5 72.018 1.26e-24 16.104
Metro_vs_SMC 0 5.781 1.43e-05 1.293
Metro_vs_SMC 1 58.932 5.58e-23 13.178
Metro_vs_SMC 2 52.641 4.71e-22 11.771
Metro_vs_SMC 3 62.281 1.96e-23 13.926
Metro_vs_SMC 4 71.069 1.62e-24 15.891
Metro_vs_SMC 5 84.899 5.57e-26 18.984
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 1.605 0.049 0.016 96.576
HMC 8 2.533 0.058 0.025 100.794
HMC 10 3.091 0.063 0.039 78.048
HMC 12 3.874 0.095 0.057 65.851
HMC 15 4.806 0.084 0.038 124.496
HMC 18 5.604 0.133 0.084 64.936
SMC 5 0.047 0.049 0.016 -0.120
SMC 8 0.074 0.058 0.025 0.629
SMC 10 0.086 0.063 0.039 0.589
SMC 12 0.088 0.095 0.057 -0.110
SMC 15 0.108 0.084 0.038 0.655
SMC 18 0.106 0.133 0.084 -0.322
Metro 5 0.645 0.049 0.016 36.998
Metro 8 2.556 0.058 0.025 101.736
Metro 10 3.213 0.063 0.039 81.189
Metro 12 3.908 0.095 0.057 66.437
Metro 15 4.656 0.084 0.038 120.549
Metro 18 5.833 0.133 0.084 67.660
DEMetro_Z 5 1.155 0.049 0.016 68.636
DEMetro_Z 8 2.460 0.058 0.025 97.835
DEMetro_Z 10 3.196 0.063 0.039 80.746
DEMetro_Z 12 3.929 0.095 0.057 66.804
DEMetro_Z 15 4.834 0.084 0.038 125.255
DEMetro_Z 18 5.663 0.133 0.084 65.641
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 119.334 9.07e-32 108.219
HMC 8 165.929 6.66e-39 103.337
HMC 10 112.486 1.41e-32 85.066
HMC 12 154.479 1.54e-47 64.903
HMC 15 109.562 1.89e-30 109.348
HMC 18 129.571 1.8e-37 74.844
SMC 5 -0.140 0.889 -0.055
SMC 8 1.338 0.189 0.461
SMC 10 2.043 0.0481 0.669
SMC 12 -0.697 0.49 -0.194
SMC 15 1.332 0.192 0.573
SMC 18 -1.402 0.17 -0.386
Metro 5 5.470 2.8e-05 40.092
Metro 8 145.871 5.45e-36 101.870
Metro 10 154.546 1.93e-40 84.705
Metro 12 110.245 2.13e-35 64.841
Metro 15 138.105 3.23e-34 108.676
Metro 18 142.851 2.38e-40 75.318
DEMetro_Z 5 6.904 1.38e-06 76.950
DEMetro_Z 8 20.875 1.33e-14 98.487
DEMetro_Z 10 152.767 5.93e-40 85.224
DEMetro_Z 12 141.822 1.08e-43 65.125
DEMetro_Z 15 109.744 1.63e-30 108.481
DEMetro_Z 18 115.462 2.34e-34 75.765
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 6.883 1.45e-06 1.539
DEMetro_Z_vs_SMC 1 21.052 1.25e-14 4.707
DEMetro_Z_vs_SMC 2 172.971 7.6e-32 38.677
DEMetro_Z_vs_SMC 3 158.547 3.97e-31 35.452
DEMetro_Z_vs_SMC 4 107.920 5.88e-28 24.132
DEMetro_Z_vs_SMC 5 119.693 8.25e-29 26.764
HMC_vs_Metro 0 9.338 1.57e-08 2.088
HMC_vs_Metro 1 2.116 0.0477 0.473
HMC_vs_Metro 2 0.466 0.646 0.104
HMC_vs_Metro 3 0.087 0.931 0.020
HMC_vs_Metro 4 0.620 0.543 0.139
HMC_vs_Metro 5 -0.785 0.442 -0.176
Metro_vs_DEMetro_Z 0 -2.320 0.0316 -0.519
Metro_vs_DEMetro_Z 1 0.707 0.488 0.158
Metro_vs_DEMetro_Z 2 -0.699 0.493 -0.156
Metro_vs_DEMetro_Z 3 -0.458 0.652 -0.102
Metro_vs_DEMetro_Z 4 0.161 0.874 0.036
Metro_vs_DEMetro_Z 5 -0.526 0.605 -0.118
HMC_vs_SMC 0 105.612 8.87e-28 23.616
HMC_vs_SMC 1 148.008 1.47e-30 33.096
HMC_vs_SMC 2 122.403 5.39e-29 27.370
HMC_vs_SMC 3 155.707 5.6e-31 34.817
HMC_vs_SMC 4 89.965 1.86e-26 20.117
HMC_vs_SMC 5 137.896 5.62e-30 30.835
Metro_vs_SMC 0 5.478 2.76e-05 1.225
Metro_vs_SMC 1 131.366 1.41e-29 29.374
Metro_vs_SMC 2 151.952 8.9e-31 33.978
Metro_vs_SMC 3 123.185 4.78e-29 27.545
Metro_vs_SMC 4 130.288 1.65e-29 29.133
Metro_vs_SMC 5 136.351 6.96e-30 30.489
HMC_vs_DEMetro_Z 0 2.725 0.0135 0.609
HMC_vs_DEMetro_Z 1 0.974 0.342 0.218
HMC_vs_DEMetro_Z 2 -0.204 0.841 -0.046
HMC_vs_DEMetro_Z 3 -0.348 0.732 -0.078
HMC_vs_DEMetro_Z 4 0.629 0.537 0.141
HMC_vs_DEMetro_Z 5 -0.939 0.36 -0.210
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.553 0.012 0.005 108.219
HMC 8 0.622 0.010 0.006 103.337
HMC 10 0.628 0.009 0.007 85.066
HMC 12 0.622 0.013 0.009 64.903
HMC 15 0.622 0.008 0.006 109.348
HMC 18 0.622 0.012 0.008 74.844
SMC 5 0.012 0.012 0.005 -0.055
SMC 8 0.013 0.010 0.006 0.461
SMC 10 0.013 0.009 0.007 0.669
SMC 12 0.011 0.013 0.009 -0.194
SMC 15 0.012 0.008 0.006 0.573
SMC 18 0.008 0.012 0.008 -0.386
Metro 5 0.213 0.012 0.005 40.092
Metro 8 0.613 0.010 0.006 101.870
Metro 10 0.625 0.009 0.007 84.705
Metro 12 0.622 0.013 0.009 64.841
Metro 15 0.619 0.008 0.006 108.676
Metro 18 0.626 0.012 0.008 75.318
DEMetro_Z 5 0.397 0.012 0.005 76.950
DEMetro_Z 8 0.593 0.010 0.006 98.487
DEMetro_Z 10 0.629 0.009 0.007 85.224
DEMetro_Z 12 0.624 0.013 0.009 65.125
DEMetro_Z 15 0.618 0.008 0.006 108.481
DEMetro_Z 18 0.630 0.012 0.008 75.765
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Varying_Mode_Distance_with_heavy_Tails (Mixture, mm, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.500 0.0178 1.062
HMC 8 3.527 0.00171 2.265
HMC 10 4.894 3.49e-05 2.355
HMC 12 4.954 6.12e-05 4.299
HMC 15 5.853 1.12e-05 12.435
HMC 18 4.641 0.000158 6.562
SMC 5 3.169 0.0038 1.679
SMC 8 3.865 0.000732 2.466
SMC 10 3.603 0.00129 1.990
SMC 12 4.095 0.000462 3.153
SMC 15 4.736 0.000125 6.293
SMC 18 4.884 8.89e-05 6.593
Metro 5 3.175 0.00461 3.387
Metro 8 3.518 0.00147 1.697
Metro 10 3.861 0.000441 1.349
Metro 12 3.299 0.0032 2.527
Metro 15 3.753 0.00116 3.650
Metro 18 5.101 2.64e-05 2.891
DEMetro_Z 5 4.665 8.74e-05 2.758
DEMetro_Z 8 6.432 2.58e-06 7.616
DEMetro_Z 10 4.766 4.78e-05 2.244
DEMetro_Z 12 7.619 2.49e-07 10.898
DEMetro_Z 15 4.941 8.85e-05 16.403
DEMetro_Z 18 5.876 1.1e-05 15.446
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.594 0.0178 -0.580
HMC_vs_DEMetro_Z 1 -3.570 0.00204 -0.798
HMC_vs_DEMetro_Z 2 0.172 0.865 0.038
HMC_vs_DEMetro_Z 3 -3.696 0.00154 -0.826
HMC_vs_DEMetro_Z 4 -0.960 0.349 -0.215
HMC_vs_DEMetro_Z 5 -2.976 0.00777 -0.665
Metro_vs_SMC 0 1.372 0.186 0.307
Metro_vs_SMC 1 -1.199 0.245 -0.268
Metro_vs_SMC 2 -1.299 0.21 -0.290
Metro_vs_SMC 3 -0.519 0.61 -0.116
Metro_vs_SMC 4 -1.630 0.12 -0.365
Metro_vs_SMC 5 -2.347 0.0299 -0.525
Metro_vs_DEMetro_Z 0 0.578 0.57 0.129
Metro_vs_DEMetro_Z 1 -5.544 2.4e-05 -1.240
Metro_vs_DEMetro_Z 2 -1.780 0.0911 -0.398
Metro_vs_DEMetro_Z 3 -6.346 4.34e-06 -1.419
Metro_vs_DEMetro_Z 4 -3.439 0.00275 -0.769
Metro_vs_DEMetro_Z 5 -5.147 5.74e-05 -1.151
HMC_vs_Metro 0 -1.928 0.0689 -0.431
HMC_vs_Metro 1 0.717 0.482 0.160
HMC_vs_Metro 2 2.370 0.0286 0.530
HMC_vs_Metro 3 1.697 0.106 0.379
HMC_vs_Metro 4 4.224 0.000459 0.945
HMC_vs_Metro 5 2.482 0.0226 0.555
HMC_vs_SMC 0 -0.999 0.331 -0.223
HMC_vs_SMC 1 -0.222 0.827 -0.050
HMC_vs_SMC 2 0.646 0.526 0.144
HMC_vs_SMC 3 1.059 0.303 0.237
HMC_vs_SMC 4 2.604 0.0175 0.582
HMC_vs_SMC 5 -0.014 0.989 -0.003
DEMetro_Z_vs_SMC 0 1.514 0.146 0.339
DEMetro_Z_vs_SMC 1 4.222 0.000461 0.944
DEMetro_Z_vs_SMC 2 0.380 0.708 0.085
DEMetro_Z_vs_SMC 3 4.358 0.000338 0.975
DEMetro_Z_vs_SMC 4 3.139 0.0054 0.702
DEMetro_Z_vs_SMC 5 2.952 0.00818 0.660
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.092 0.053 0.036 1.062
HMC 8 0.157 0.058 0.044 2.265
HMC 10 0.359 0.096 0.112 2.355
HMC 12 0.383 0.108 0.064 4.299
HMC 15 1.035 0.113 0.074 12.435
HMC 18 0.858 0.135 0.110 6.562
SMC 5 0.114 0.053 0.036 1.679
SMC 8 0.166 0.058 0.044 2.466
SMC 10 0.318 0.096 0.112 1.990
SMC 12 0.309 0.108 0.064 3.153
SMC 15 0.580 0.113 0.074 6.293
SMC 18 0.861 0.135 0.110 6.593
Metro 5 0.176 0.053 0.036 3.387
Metro 8 0.132 0.058 0.044 1.697
Metro 10 0.247 0.096 0.112 1.349
Metro 12 0.269 0.108 0.064 2.527
Metro 15 0.384 0.113 0.074 3.650
Metro 18 0.453 0.135 0.110 2.891
DEMetro_Z 5 0.153 0.053 0.036 2.758
DEMetro_Z 8 0.390 0.058 0.044 7.616
DEMetro_Z 10 0.347 0.096 0.112 2.244
DEMetro_Z 12 0.805 0.108 0.064 10.898
DEMetro_Z 15 1.330 0.113 0.074 16.403
DEMetro_Z 18 1.837 0.135 0.110 15.446
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 -1.505 0.149 -0.337
HMC 8 1.639 0.113 0.934
HMC 10 -0.792 0.437 -0.181
HMC 12 -1.230 0.232 -0.285
HMC 15 0.747 0.463 0.571
HMC 18 0.984 0.335 0.581
SMC 5 -1.434 0.168 -0.322
SMC 8 1.639 0.112 0.749
SMC 10 -0.768 0.451 -0.175
SMC 12 -1.516 0.146 -0.341
SMC 15 -1.087 0.29 -0.249
SMC 18 0.860 0.397 0.220
Metro 5 -1.119 0.275 -0.260
Metro 8 1.380 0.179 0.779
Metro 10 -0.776 0.447 -0.177
Metro 12 -1.428 0.169 -0.322
Metro 15 -0.878 0.388 -0.211
Metro 18 0.088 0.931 0.024
DEMetro_Z 5 -1.441 0.166 -0.323
DEMetro_Z 8 2.025 0.0531 1.101
DEMetro_Z 10 -0.788 0.44 -0.180
DEMetro_Z 12 -1.265 0.221 -0.285
DEMetro_Z 15 0.058 0.954 0.015
DEMetro_Z 18 2.548 0.0152 0.891
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.653 0.521 -0.146
HMC_vs_SMC 1 0.612 0.548 0.137
HMC_vs_SMC 2 -1.899 0.0728 -0.425
HMC_vs_SMC 3 0.924 0.367 0.207
HMC_vs_SMC 4 1.130 0.273 0.253
HMC_vs_SMC 5 0.727 0.476 0.163
Metro_vs_DEMetro_Z 0 0.949 0.355 0.212
Metro_vs_DEMetro_Z 1 -1.103 0.284 -0.247
Metro_vs_DEMetro_Z 2 0.745 0.466 0.167
Metro_vs_DEMetro_Z 3 -3.467 0.00258 -0.775
Metro_vs_DEMetro_Z 4 -1.937 0.0678 -0.433
Metro_vs_DEMetro_Z 5 -2.735 0.0132 -0.612
HMC_vs_Metro 0 -1.199 0.245 -0.268
HMC_vs_Metro 1 0.348 0.732 0.078
HMC_vs_Metro 2 -1.079 0.294 -0.241
HMC_vs_Metro 3 0.615 0.546 0.138
HMC_vs_Metro 4 1.056 0.304 0.236
HMC_vs_Metro 5 0.990 0.334 0.221
HMC_vs_DEMetro_Z 0 -1.593 0.128 -0.356
HMC_vs_DEMetro_Z 1 -0.445 0.662 -0.099
HMC_vs_DEMetro_Z 2 -0.736 0.471 -0.165
HMC_vs_DEMetro_Z 3 0.003 0.998 0.001
HMC_vs_DEMetro_Z 4 0.734 0.472 0.164
HMC_vs_DEMetro_Z 5 -0.529 0.603 -0.118
Metro_vs_SMC 0 0.917 0.37 0.205
Metro_vs_SMC 1 0.094 0.926 0.021
Metro_vs_SMC 2 -0.452 0.657 -0.101
Metro_vs_SMC 3 1.270 0.219 0.284
Metro_vs_SMC 4 0.467 0.646 0.104
Metro_vs_SMC 5 -1.111 0.28 -0.248
DEMetro_Z_vs_SMC 0 -0.058 0.955 -0.013
DEMetro_Z_vs_SMC 1 1.504 0.149 0.336
DEMetro_Z_vs_SMC 2 -1.592 0.128 -0.356
DEMetro_Z_vs_SMC 3 4.352 0.000343 0.973
DEMetro_Z_vs_SMC 4 2.295 0.0333 0.513
DEMetro_Z_vs_SMC 5 2.275 0.0346 0.509
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 3.673 17.284 40.350 -0.337
HMC 8 5.725 3.215 2.688 0.934
HMC 10 20.587 87.229 368.626 -0.181
HMC 12 6.550 19.100 44.067 -0.285
HMC 15 16.734 8.635 14.171 0.571
HMC 18 9.289 5.445 6.620 0.581
SMC 5 4.307 17.284 40.350 -0.322
SMC 8 5.228 3.215 2.688 0.749
SMC 10 22.668 87.229 368.626 -0.175
SMC 12 4.091 19.100 44.067 -0.341
SMC 15 5.110 8.635 14.171 -0.249
SMC 18 6.903 5.445 6.620 0.220
Metro 5 6.786 17.284 40.350 -0.260
Metro 8 5.308 3.215 2.688 0.779
Metro 10 21.972 87.229 368.626 -0.177
Metro 12 4.914 19.100 44.067 -0.322
Metro 15 5.642 8.635 14.171 -0.211
Metro 18 5.602 5.445 6.620 0.024
DEMetro_Z 5 4.247 17.284 40.350 -0.323
DEMetro_Z 8 6.175 3.215 2.688 1.101
DEMetro_Z 10 20.957 87.229 368.626 -0.180
DEMetro_Z 12 6.542 19.100 44.067 -0.285
DEMetro_Z 15 8.841 8.635 14.171 0.015
DEMetro_Z 18 11.341 5.445 6.620 0.891
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.518 0.0161 0.773
HMC 8 4.603 0.000127 3.380
HMC 10 4.868 3.2e-05 2.151
HMC 12 4.683 0.000117 4.041
HMC 15 5.888 1.06e-05 13.654
HMC 18 5.003 7.13e-05 8.316
SMC 5 5.223 2.19e-05 3.224
SMC 8 6.901 5.97e-07 5.529
SMC 10 7.921 8.75e-09 3.687
SMC 12 6.327 1.88e-06 4.581
SMC 15 6.173 4.92e-06 8.469
SMC 18 7.125 7.08e-07 11.223
Metro 5 3.774 0.000911 2.371
Metro 8 6.021 2.47e-06 3.442
Metro 10 4.949 1.62e-05 1.689
Metro 12 4.007 0.00053 2.692
Metro 15 4.133 0.000486 4.508
Metro 18 6.078 3e-06 4.096
DEMetro_Z 5 6.209 4.27e-07 2.365
DEMetro_Z 8 7.629 2.4e-07 10.566
DEMetro_Z 10 5.869 2.21e-06 2.757
DEMetro_Z 12 8.166 8.22e-08 10.946
DEMetro_Z 15 5.086 6.4e-05 17.001
DEMetro_Z 18 6.334 4.24e-06 19.842
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.010 0.992 0.002
Metro_vs_DEMetro_Z 1 -5.479 2.76e-05 -1.225
Metro_vs_DEMetro_Z 2 -2.280 0.0343 -0.510
Metro_vs_DEMetro_Z 3 -6.500 3.16e-06 -1.453
Metro_vs_DEMetro_Z 4 -3.289 0.00386 -0.735
Metro_vs_DEMetro_Z 5 -5.403 3.26e-05 -1.208
DEMetro_Z_vs_SMC 0 -1.189 0.249 -0.266
DEMetro_Z_vs_SMC 1 3.864 0.00104 0.864
DEMetro_Z_vs_SMC 2 -1.564 0.134 -0.350
DEMetro_Z_vs_SMC 3 3.786 0.00125 0.846
DEMetro_Z_vs_SMC 4 2.601 0.0176 0.582
DEMetro_Z_vs_SMC 5 2.452 0.0241 0.548
HMC_vs_DEMetro_Z 0 -4.394 0.000312 -0.983
HMC_vs_DEMetro_Z 1 -4.001 0.000765 -0.895
HMC_vs_DEMetro_Z 2 -1.075 0.296 -0.240
HMC_vs_DEMetro_Z 3 -4.191 0.000495 -0.937
HMC_vs_DEMetro_Z 4 -0.760 0.457 -0.170
HMC_vs_DEMetro_Z 5 -3.350 0.00337 -0.749
HMC_vs_Metro 0 -2.534 0.0202 -0.567
HMC_vs_Metro 1 -0.064 0.949 -0.014
HMC_vs_Metro 2 1.272 0.219 0.284
HMC_vs_Metro 3 1.362 0.189 0.304
HMC_vs_Metro 4 4.041 0.000698 0.904
HMC_vs_Metro 5 2.381 0.0279 0.532
HMC_vs_SMC 0 -4.617 0.000188 -1.032
HMC_vs_SMC 1 -1.923 0.0696 -0.430
HMC_vs_SMC 2 -3.537 0.0022 -0.791
HMC_vs_SMC 3 -0.491 0.629 -0.110
HMC_vs_SMC 4 2.033 0.0562 0.455
HMC_vs_SMC 5 -1.177 0.254 -0.263
Metro_vs_SMC 0 -0.921 0.368 -0.206
Metro_vs_SMC 1 -2.520 0.0208 -0.564
Metro_vs_SMC 2 -6.005 8.89e-06 -1.343
Metro_vs_SMC 3 -1.729 0.1 -0.387
Metro_vs_SMC 4 -2.278 0.0345 -0.509
Metro_vs_SMC 5 -3.848 0.00108 -0.861
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.179 0.135 0.057 0.773
HMC 8 0.247 0.133 0.034 3.380
HMC 10 0.412 0.171 0.112 2.151
HMC 12 0.435 0.191 0.060 4.041
HMC 15 1.067 0.176 0.065 13.654
HMC 18 0.865 0.213 0.078 8.316
SMC 5 0.319 0.135 0.057 3.224
SMC 8 0.319 0.133 0.034 5.529
SMC 10 0.585 0.171 0.112 3.687
SMC 12 0.468 0.191 0.060 4.581
SMC 15 0.729 0.176 0.065 8.469
SMC 18 1.092 0.213 0.078 11.223
Metro 5 0.270 0.135 0.057 2.371
Metro 8 0.249 0.133 0.034 3.442
Metro 10 0.361 0.171 0.112 1.689
Metro 12 0.353 0.191 0.060 2.692
Metro 15 0.470 0.176 0.065 4.508
Metro 18 0.534 0.213 0.078 4.096
DEMetro_Z 5 0.270 0.135 0.057 2.365
DEMetro_Z 8 0.489 0.133 0.034 10.566
DEMetro_Z 10 0.480 0.171 0.112 2.757
DEMetro_Z 12 0.853 0.191 0.060 10.946
DEMetro_Z 15 1.285 0.176 0.065 17.001
DEMetro_Z 18 1.768 0.213 0.078 19.842
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.584 8.95e-05 2.342
HMC 8 4.051 0.000531 3.315
HMC 10 5.609 1.81e-05 9.066
HMC 12 4.545 0.000194 5.994
HMC 15 5.584 2.09e-05 15.611
HMC 18 4.722 0.000137 8.339
SMC 5 5.861 8.63e-06 6.391
SMC 8 5.098 3.94e-05 3.948
SMC 10 6.414 3.09e-06 9.911
SMC 12 5.123 4.53e-05 5.217
SMC 15 5.241 4.06e-05 7.925
SMC 18 5.084 5.94e-05 8.544
Metro 5 4.947 3.91e-05 2.783
Metro 8 4.354 0.000159 2.137
Metro 10 6.221 2.5e-06 4.603
Metro 12 3.748 0.00118 3.731
Metro 15 3.593 0.00177 4.267
Metro 18 4.912 5.49e-05 3.354
DEMetro_Z 5 5.716 1.05e-05 5.217
DEMetro_Z 8 7.377 3.98e-07 10.306
DEMetro_Z 10 6.025 7.15e-06 9.391
DEMetro_Z 12 7.086 8.58e-07 15.468
DEMetro_Z 15 4.591 0.000197 20.757
DEMetro_Z 18 5.813 1.3e-05 21.832
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -0.771 0.45 -0.172
DEMetro_Z_vs_SMC 1 4.538 0.000225 1.015
DEMetro_Z_vs_SMC 2 -0.233 0.819 -0.052
DEMetro_Z_vs_SMC 3 3.920 0.00092 0.876
DEMetro_Z_vs_SMC 4 2.978 0.00773 0.666
DEMetro_Z_vs_SMC 5 3.188 0.00484 0.713
HMC_vs_Metro 0 -0.638 0.531 -0.143
HMC_vs_Metro 1 1.342 0.195 0.300
HMC_vs_Metro 2 2.613 0.0171 0.584
HMC_vs_Metro 3 1.463 0.16 0.327
HMC_vs_Metro 4 4.058 0.000671 0.907
HMC_vs_Metro 5 2.617 0.017 0.585
Metro_vs_DEMetro_Z 0 -2.265 0.0354 -0.507
Metro_vs_DEMetro_Z 1 -6.102 7.23e-06 -1.365
Metro_vs_DEMetro_Z 2 -2.953 0.00817 -0.660
Metro_vs_DEMetro_Z 3 -5.447 2.96e-05 -1.218
Metro_vs_DEMetro_Z 4 -3.327 0.00355 -0.744
Metro_vs_DEMetro_Z 5 -5.269 4.38e-05 -1.178
HMC_vs_SMC 0 -3.944 0.000871 -0.882
HMC_vs_SMC 1 -0.543 0.594 -0.121
HMC_vs_SMC 2 -0.444 0.662 -0.099
HMC_vs_SMC 3 0.496 0.626 0.111
HMC_vs_SMC 4 2.516 0.021 0.563
HMC_vs_SMC 5 -0.078 0.939 -0.017
Metro_vs_SMC 0 -2.899 0.00919 -0.648
Metro_vs_SMC 1 -2.536 0.0201 -0.567
Metro_vs_SMC 2 -3.126 0.00556 -0.699
Metro_vs_SMC 3 -0.933 0.363 -0.209
Metro_vs_SMC 4 -1.968 0.0638 -0.440
Metro_vs_SMC 5 -2.711 0.0139 -0.606
HMC_vs_DEMetro_Z 0 -2.887 0.00945 -0.646
HMC_vs_DEMetro_Z 1 -3.616 0.00184 -0.808
HMC_vs_DEMetro_Z 2 -0.134 0.895 -0.030
HMC_vs_DEMetro_Z 3 -3.448 0.0027 -0.771
HMC_vs_DEMetro_Z 4 -0.915 0.372 -0.205
HMC_vs_DEMetro_Z 5 -3.228 0.00443 -0.722
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.023 0.012 0.005 2.342
HMC 8 0.031 0.012 0.006 3.315
HMC 10 0.053 0.011 0.005 9.066
HMC 12 0.047 0.013 0.006 5.994
HMC 15 0.114 0.010 0.007 15.611
HMC 18 0.079 0.013 0.008 8.339
SMC 5 0.042 0.012 0.005 6.391
SMC 8 0.034 0.012 0.006 3.948
SMC 10 0.056 0.011 0.005 9.911
SMC 12 0.043 0.013 0.006 5.217
SMC 15 0.063 0.010 0.007 7.925
SMC 18 0.080 0.013 0.008 8.544
Metro 5 0.025 0.012 0.005 2.783
Metro 8 0.024 0.012 0.006 2.137
Metro 10 0.032 0.011 0.005 4.603
Metro 12 0.034 0.013 0.006 3.731
Metro 15 0.039 0.010 0.007 4.267
Metro 18 0.039 0.013 0.008 3.354
DEMetro_Z 5 0.037 0.012 0.005 5.217
DEMetro_Z 8 0.070 0.012 0.006 10.306
DEMetro_Z 10 0.054 0.011 0.005 9.391
DEMetro_Z 12 0.102 0.013 0.006 15.468
DEMetro_Z 15 0.148 0.010 0.007 20.757
DEMetro_Z 18 0.186 0.013 0.008 21.832
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.092 0.00452 1.585
HMC 8 4.470 0.000206 4.229
HMC 10 3.814 0.000704 1.942
HMC 12 4.460 0.000207 4.031
HMC 15 5.174 4.6e-05 7.193
HMC 18 4.742 0.00013 8.163
SMC 5 2.466 0.0188 0.947
SMC 8 4.868 8.27e-05 4.942
SMC 10 4.054 0.00057 4.033
SMC 12 3.199 0.0038 2.013
SMC 15 4.261 0.0004 8.090
SMC 18 4.200 0.000444 6.064
Metro 5 4.469 0.000116 2.195
Metro 8 4.678 7.9e-05 2.620
Metro 10 2.497 0.017 0.797
Metro 12 1.423 0.171 3.854
Metro 15 4.231 0.000384 4.575
Metro 18 4.352 0.000263 3.775
DEMetro_Z 5 3.702 0.00124 3.029
DEMetro_Z 8 4.424 0.000211 3.545
DEMetro_Z 10 4.512 0.000172 3.680
DEMetro_Z 12 4.874 9.34e-05 7.248
DEMetro_Z 15 4.433 0.000279 13.631
DEMetro_Z 18 6.099 6.46e-06 11.621
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.620 0.122 -0.362
HMC_vs_DEMetro_Z 1 0.533 0.6 0.119
HMC_vs_DEMetro_Z 2 -1.756 0.0951 -0.393
HMC_vs_DEMetro_Z 3 -1.945 0.0667 -0.435
HMC_vs_DEMetro_Z 4 -2.053 0.0541 -0.459
HMC_vs_DEMetro_Z 5 -1.264 0.222 -0.283
Metro_vs_SMC 0 2.476 0.0229 0.554
Metro_vs_SMC 1 -2.187 0.0414 -0.489
Metro_vs_SMC 2 -3.158 0.00518 -0.706
Metro_vs_SMC 3 0.669 0.512 0.149
Metro_vs_SMC 4 -1.561 0.135 -0.349
Metro_vs_SMC 5 -1.430 0.169 -0.320
Metro_vs_DEMetro_Z 0 -1.108 0.282 -0.248
Metro_vs_DEMetro_Z 1 -1.067 0.3 -0.238
Metro_vs_DEMetro_Z 2 -3.596 0.00193 -0.804
Metro_vs_DEMetro_Z 3 -0.996 0.332 -0.223
Metro_vs_DEMetro_Z 4 -2.823 0.0109 -0.631
Metro_vs_DEMetro_Z 5 -3.709 0.00149 -0.829
HMC_vs_Metro 0 -0.853 0.404 -0.191
HMC_vs_Metro 1 1.461 0.16 0.327
HMC_vs_Metro 2 2.492 0.0221 0.557
HMC_vs_Metro 3 0.058 0.954 0.013
HMC_vs_Metro 4 2.242 0.0371 0.501
HMC_vs_Metro 5 2.431 0.0251 0.544
HMC_vs_SMC 0 1.011 0.325 0.226
HMC_vs_SMC 1 -0.457 0.653 -0.102
HMC_vs_SMC 2 -2.024 0.0573 -0.453
HMC_vs_SMC 3 1.845 0.0806 0.413
HMC_vs_SMC 4 -0.374 0.713 -0.084
HMC_vs_SMC 5 0.916 0.371 0.205
DEMetro_Z_vs_SMC 0 2.481 0.0226 0.555
DEMetro_Z_vs_SMC 1 -1.061 0.302 -0.237
DEMetro_Z_vs_SMC 2 -0.286 0.778 -0.064
DEMetro_Z_vs_SMC 3 3.524 0.00227 0.788
DEMetro_Z_vs_SMC 4 1.380 0.184 0.309
DEMetro_Z_vs_SMC 5 2.356 0.0294 0.527
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.111 0.053 0.036 1.585
HMC 8 0.242 0.058 0.044 4.229
HMC 10 0.313 0.096 0.112 1.942
HMC 12 0.366 0.108 0.064 4.031
HMC 15 0.646 0.113 0.074 7.193
HMC 18 1.034 0.135 0.110 8.163
SMC 5 0.088 0.053 0.036 0.947
SMC 8 0.273 0.058 0.044 4.942
SMC 10 0.547 0.096 0.112 4.033
SMC 12 0.236 0.108 0.064 2.013
SMC 15 0.713 0.113 0.074 8.090
SMC 18 0.803 0.135 0.110 6.064
Metro 5 0.133 0.053 0.036 2.195
Metro 8 0.172 0.058 0.044 2.620
Metro 10 0.185 0.096 0.112 0.797
Metro 12 0.354 0.108 0.064 3.854
Metro 15 0.452 0.113 0.074 4.575
Metro 18 0.551 0.135 0.110 3.775
DEMetro_Z 5 0.163 0.053 0.036 3.029
DEMetro_Z 8 0.213 0.058 0.044 3.545
DEMetro_Z 10 0.507 0.096 0.112 3.680
DEMetro_Z 12 0.571 0.108 0.064 7.248
DEMetro_Z 15 1.124 0.113 0.074 13.631
DEMetro_Z 18 1.415 0.135 0.110 11.621
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 -1.420 0.171 -0.320
HMC 8 1.283 0.21 0.664
HMC 10 -0.800 0.433 -0.182
HMC 12 -1.313 0.204 -0.296
HMC 15 -0.899 0.378 -0.211
HMC 18 0.674 0.505 0.206
SMC 5 -1.610 0.124 -0.360
SMC 8 0.647 0.522 0.290
SMC 10 -0.785 0.442 -0.179
SMC 12 -1.477 0.156 -0.333
SMC 15 -0.735 0.47 -0.169
SMC 18 -0.120 0.905 -0.031
Metro 5 -1.534 0.141 -0.344
Metro 8 2.460 0.0208 1.349
Metro 10 -0.792 0.437 -0.181
Metro 12 0.160 0.874 0.071
Metro 15 0.174 0.863 0.069
Metro 18 -0.192 0.849 -0.052
DEMetro_Z 5 -1.437 0.167 -0.323
DEMetro_Z 8 1.794 0.0844 1.002
DEMetro_Z 10 -0.690 0.498 -0.158
DEMetro_Z 12 -1.377 0.184 -0.310
DEMetro_Z 15 0.027 0.978 0.007
DEMetro_Z 18 1.494 0.143 0.480
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.331 0.199 0.298
HMC_vs_SMC 1 1.986 0.0617 0.444
HMC_vs_SMC 2 -2.306 0.0325 -0.516
HMC_vs_SMC 3 1.808 0.0865 0.404
HMC_vs_SMC 4 -0.588 0.563 -0.132
HMC_vs_SMC 5 0.940 0.359 0.210
Metro_vs_DEMetro_Z 0 -1.862 0.0781 -0.416
Metro_vs_DEMetro_Z 1 1.173 0.255 0.262
Metro_vs_DEMetro_Z 2 -1.093 0.288 -0.244
Metro_vs_DEMetro_Z 3 1.016 0.322 0.227
Metro_vs_DEMetro_Z 4 0.174 0.864 0.039
Metro_vs_DEMetro_Z 5 -2.118 0.0476 -0.474
HMC_vs_Metro 0 0.801 0.433 0.179
HMC_vs_Metro 1 -2.373 0.0283 -0.531
HMC_vs_Metro 2 -1.423 0.171 -0.318
HMC_vs_Metro 3 -0.979 0.34 -0.219
HMC_vs_Metro 4 -0.864 0.398 -0.193
HMC_vs_Metro 5 0.938 0.36 0.210
HMC_vs_DEMetro_Z 0 0.079 0.938 0.018
HMC_vs_DEMetro_Z 1 -2.074 0.0519 -0.464
HMC_vs_DEMetro_Z 2 -1.182 0.252 -0.264
HMC_vs_DEMetro_Z 3 0.827 0.418 0.185
HMC_vs_DEMetro_Z 4 -1.849 0.0801 -0.413
HMC_vs_DEMetro_Z 5 -0.856 0.403 -0.191
Metro_vs_SMC 0 0.993 0.333 0.222
Metro_vs_SMC 1 3.992 0.000781 0.893
Metro_vs_SMC 2 -1.259 0.223 -0.281
Metro_vs_SMC 3 1.077 0.295 0.241
Metro_vs_SMC 4 0.707 0.488 0.158
Metro_vs_SMC 5 -0.106 0.917 -0.024
DEMetro_Z_vs_SMC 0 2.212 0.0394 0.495
DEMetro_Z_vs_SMC 1 3.983 0.000797 0.891
DEMetro_Z_vs_SMC 2 0.995 0.332 0.222
DEMetro_Z_vs_SMC 3 1.607 0.124 0.359
DEMetro_Z_vs_SMC 4 1.429 0.169 0.320
DEMetro_Z_vs_SMC 5 2.039 0.0556 0.456
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 4.368 17.284 40.350 -0.320
HMC 8 4.999 3.215 2.688 0.664
HMC 10 19.988 87.229 368.626 -0.182
HMC 12 6.044 19.100 44.067 -0.296
HMC 15 5.639 8.635 14.171 -0.211
HMC 18 6.807 5.445 6.620 0.206
SMC 5 2.746 17.284 40.350 -0.360
SMC 8 3.994 3.215 2.688 0.290
SMC 10 21.277 87.229 368.626 -0.179
SMC 12 4.438 19.100 44.067 -0.333
SMC 15 6.237 8.635 14.171 -0.169
SMC 18 5.240 5.445 6.620 -0.031
Metro 5 3.403 17.284 40.350 -0.344
Metro 8 6.842 3.215 2.688 1.349
Metro 10 20.615 87.229 368.626 -0.181
Metro 12 22.222 19.100 44.067 0.071
Metro 15 9.609 8.635 14.171 0.069
Metro 18 5.104 5.445 6.620 -0.052
DEMetro_Z 5 4.271 17.284 40.350 -0.323
DEMetro_Z 8 5.907 3.215 2.688 1.002
DEMetro_Z 10 28.997 87.229 368.626 -0.158
DEMetro_Z 12 5.432 19.100 44.067 -0.310
DEMetro_Z 15 8.735 8.635 14.171 0.007
DEMetro_Z 18 8.625 5.445 6.620 0.480
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.357 0.0239 0.846
HMC 8 5.578 1.58e-05 5.699
HMC 10 3.912 0.000483 1.767
HMC 12 4.636 0.000129 3.904
HMC 15 5.263 3.86e-05 7.941
HMC 18 4.881 9.79e-05 10.499
SMC 5 2.862 0.00689 0.987
SMC 8 7.341 3.24e-07 7.457
SMC 10 5.284 2.83e-05 4.700
SMC 12 5.994 2.44e-06 3.312
SMC 15 5.445 2.7e-05 10.352
SMC 18 5.724 1.38e-05 8.855
Metro 5 4.700 3.65e-05 1.669
Metro 8 8.181 9.65e-09 4.392
Metro 10 3.395 0.00176 0.927
Metro 12 1.631 0.119 4.778
Metro 15 4.879 8.24e-05 5.196
Metro 18 4.984 6.04e-05 4.720
DEMetro_Z 5 4.927 3.22e-05 2.388
DEMetro_Z 8 5.619 1.5e-05 6.139
DEMetro_Z 10 4.692 0.000111 3.856
DEMetro_Z 12 5.269 3.69e-05 7.191
DEMetro_Z 15 4.874 0.000102 15.114
DEMetro_Z 18 6.422 3.39e-06 14.919
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.438 0.167 -0.321
Metro_vs_DEMetro_Z 1 -1.411 0.174 -0.315
Metro_vs_DEMetro_Z 2 -3.605 0.00189 -0.806
Metro_vs_DEMetro_Z 3 -0.692 0.497 -0.155
Metro_vs_DEMetro_Z 4 -3.079 0.00618 -0.689
Metro_vs_DEMetro_Z 5 -4.296 0.00039 -0.961
DEMetro_Z_vs_SMC 0 3.655 0.00168 0.817
DEMetro_Z_vs_SMC 1 -0.995 0.332 -0.223
DEMetro_Z_vs_SMC 2 -0.707 0.488 -0.158
DEMetro_Z_vs_SMC 3 2.710 0.0139 0.606
DEMetro_Z_vs_SMC 4 1.173 0.255 0.262
DEMetro_Z_vs_SMC 5 2.211 0.0395 0.494
HMC_vs_DEMetro_Z 0 -2.772 0.0121 -0.620
HMC_vs_DEMetro_Z 1 -0.277 0.784 -0.062
HMC_vs_DEMetro_Z 2 -2.249 0.0366 -0.503
HMC_vs_DEMetro_Z 3 -2.083 0.051 -0.466
HMC_vs_DEMetro_Z 4 -2.276 0.0346 -0.509
HMC_vs_DEMetro_Z 5 -1.278 0.217 -0.286
HMC_vs_Metro 0 -1.915 0.0706 -0.428
HMC_vs_Metro 1 1.178 0.253 0.263
HMC_vs_Metro 2 2.086 0.0507 0.466
HMC_vs_Metro 3 -0.281 0.782 -0.063
HMC_vs_Metro 4 2.200 0.0404 0.492
HMC_vs_Metro 5 2.497 0.0219 0.558
HMC_vs_SMC 0 -0.347 0.733 -0.078
HMC_vs_SMC 1 -1.059 0.303 -0.237
HMC_vs_SMC 2 -3.121 0.00562 -0.698
HMC_vs_SMC 3 0.591 0.561 0.132
HMC_vs_SMC 4 -0.940 0.359 -0.210
HMC_vs_SMC 5 0.634 0.534 0.142
Metro_vs_SMC 0 2.191 0.0411 0.490
Metro_vs_SMC 1 -2.736 0.0131 -0.612
Metro_vs_SMC 2 -4.177 0.000511 -0.934
Metro_vs_SMC 3 0.494 0.627 0.110
Metro_vs_SMC 4 -2.230 0.038 -0.499
Metro_vs_SMC 5 -2.393 0.0272 -0.535
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.183 0.135 0.057 0.846
HMC 8 0.325 0.133 0.034 5.699
HMC 10 0.369 0.171 0.112 1.767
HMC 12 0.427 0.191 0.060 3.904
HMC 15 0.694 0.176 0.065 7.941
HMC 18 1.036 0.213 0.078 10.499
SMC 5 0.191 0.135 0.057 0.987
SMC 8 0.384 0.133 0.034 7.457
SMC 10 0.698 0.171 0.112 4.700
SMC 12 0.391 0.191 0.060 3.312
SMC 15 0.851 0.176 0.065 10.352
SMC 18 0.907 0.213 0.078 8.855
Metro 5 0.230 0.135 0.057 1.669
Metro 8 0.281 0.133 0.034 4.392
Metro 10 0.275 0.171 0.112 0.927
Metro 12 0.480 0.191 0.060 4.778
Metro 15 0.515 0.176 0.065 5.196
Metro 18 0.583 0.213 0.078 4.720
DEMetro_Z 5 0.271 0.135 0.057 2.388
DEMetro_Z 8 0.340 0.133 0.034 6.139
DEMetro_Z 10 0.603 0.171 0.112 3.856
DEMetro_Z 12 0.626 0.191 0.060 7.191
DEMetro_Z 15 1.162 0.176 0.065 15.114
DEMetro_Z 18 1.382 0.213 0.078 14.919
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.091 0.000447 2.937
HMC 8 4.443 0.000251 6.284
HMC 10 4.734 0.000132 7.895
HMC 12 4.979 6.81e-05 5.877
HMC 15 5.151 5.1e-05 8.626
HMC 18 4.686 0.000153 10.539
SMC 5 4.028 0.000513 2.793
SMC 8 5.435 2.53e-05 7.426
SMC 10 4.664 0.000166 17.094
SMC 12 4.749 9.82e-05 3.993
SMC 15 4.235 0.000435 10.728
SMC 18 4.208 0.000453 8.150
Metro 5 5.770 6.01e-06 3.753
Metro 8 4.589 0.0001 2.581
Metro 10 4.842 5.32e-05 2.785
Metro 12 4.248 0.000249 2.421
Metro 15 4.611 0.000143 4.155
Metro 18 4.408 0.000241 4.261
DEMetro_Z 5 5.098 3.33e-05 3.389
DEMetro_Z 8 4.375 0.000274 4.762
DEMetro_Z 10 5.480 2.5e-05 10.399
DEMetro_Z 12 4.511 0.000229 10.400
DEMetro_Z 15 4.238 0.00044 17.736
DEMetro_Z 18 5.481 2.63e-05 15.224
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 0.817 0.424 0.183
DEMetro_Z_vs_SMC 1 -1.578 0.131 -0.353
DEMetro_Z_vs_SMC 2 -1.861 0.0783 -0.416
DEMetro_Z_vs_SMC 3 2.753 0.0126 0.616
DEMetro_Z_vs_SMC 4 1.284 0.215 0.287
DEMetro_Z_vs_SMC 5 2.088 0.0505 0.467
HMC_vs_Metro 0 -0.808 0.429 -0.181
HMC_vs_Metro 1 2.631 0.0165 0.588
HMC_vs_Metro 2 3.212 0.00458 0.718
HMC_vs_Metro 3 2.763 0.0124 0.618
HMC_vs_Metro 4 2.912 0.00894 0.651
HMC_vs_Metro 5 2.674 0.015 0.598
Metro_vs_DEMetro_Z 0 0.450 0.657 0.101
Metro_vs_DEMetro_Z 1 -1.843 0.081 -0.412
Metro_vs_DEMetro_Z 2 -4.296 0.00039 -0.961
Metro_vs_DEMetro_Z 3 -3.282 0.00392 -0.734
Metro_vs_DEMetro_Z 4 -3.292 0.00383 -0.736
Metro_vs_DEMetro_Z 5 -3.925 0.00091 -0.878
HMC_vs_SMC 0 0.142 0.889 0.032
HMC_vs_SMC 1 -0.507 0.618 -0.113
HMC_vs_SMC 2 -2.297 0.0331 -0.514
HMC_vs_SMC 3 1.280 0.216 0.286
HMC_vs_SMC 4 -0.663 0.515 -0.148
HMC_vs_SMC 5 0.788 0.44 0.176
Metro_vs_SMC 0 1.140 0.268 0.255
Metro_vs_SMC 1 -3.724 0.00144 -0.833
Metro_vs_SMC 2 -3.691 0.00155 -0.825
Metro_vs_SMC 3 -1.415 0.173 -0.317
Metro_vs_SMC 4 -2.253 0.0363 -0.504
Metro_vs_SMC 5 -1.877 0.0759 -0.420
HMC_vs_DEMetro_Z 0 -0.418 0.681 -0.093
HMC_vs_DEMetro_Z 1 0.782 0.444 0.175
HMC_vs_DEMetro_Z 2 -0.998 0.331 -0.223
HMC_vs_DEMetro_Z 3 -1.771 0.0927 -0.396
HMC_vs_DEMetro_Z 4 -2.206 0.0399 -0.493
HMC_vs_DEMetro_Z 5 -1.209 0.241 -0.270
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.026 0.012 0.005 2.937
HMC 8 0.047 0.012 0.006 6.284
HMC 10 0.047 0.011 0.005 7.895
HMC 12 0.047 0.013 0.006 5.877
HMC 15 0.067 0.010 0.007 8.626
HMC 18 0.096 0.013 0.008 10.539
SMC 5 0.025 0.012 0.005 2.793
SMC 8 0.054 0.012 0.006 7.426
SMC 10 0.090 0.011 0.005 17.094
SMC 12 0.036 0.013 0.006 3.993
SMC 15 0.081 0.010 0.007 10.728
SMC 18 0.077 0.013 0.008 8.150
Metro 5 0.030 0.012 0.005 3.753
Metro 8 0.027 0.012 0.006 2.581
Metro 10 0.024 0.011 0.005 2.785
Metro 12 0.027 0.013 0.006 2.421
Metro 15 0.038 0.010 0.007 4.155
Metro 18 0.047 0.013 0.008 4.261
DEMetro_Z 5 0.028 0.012 0.005 3.389
DEMetro_Z 8 0.039 0.012 0.006 4.762
DEMetro_Z 10 0.059 0.011 0.005 10.399
DEMetro_Z 12 0.073 0.013 0.006 10.400
DEMetro_Z 15 0.128 0.010 0.007 17.736
DEMetro_Z 18 0.133 0.013 0.008 15.224
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Tails

▼

Varying_only_Tails (MvStudentT, nu, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.051 0.96 -0.016
HMC 3.0 1.689 0.0996 0.574
HMC 4.0 -0.465 0.645 -0.152
HMC 10.0 -0.383 0.704 -0.110
HMC 50.0 -1.990 0.0545 -0.549
SMC 2.1 2.419 0.0219 1.109
SMC 3.0 -0.368 0.715 -0.119
SMC 4.0 1.279 0.209 0.416
SMC 10.0 -1.027 0.311 -0.298
SMC 50.0 -1.388 0.174 -0.386
Metro 2.1 1.569 0.125 0.538
Metro 3.0 2.606 0.0139 1.114
Metro 4.0 3.390 0.00241 2.192
Metro 10.0 2.411 0.0209 0.741
Metro 50.0 1.668 0.105 0.662
DEMetro_Z 2.1 4.029 0.000387 1.999
DEMetro_Z 3.0 3.095 0.00472 1.780
DEMetro_Z 4.0 4.502 0.000118 2.400
DEMetro_Z 10.0 2.991 0.00591 1.595
DEMetro_Z 50.0 3.205 0.00311 1.392
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -5.007 7.83e-05 -1.120
HMC_vs_DEMetro_Z 1 -1.916 0.0705 -0.428
HMC_vs_DEMetro_Z 2 -4.854 0.00011 -1.085
HMC_vs_DEMetro_Z 3 -3.145 0.00533 -0.703
HMC_vs_DEMetro_Z 4 -4.781 0.00013 -1.069
Metro_vs_SMC 0 -1.329 0.2 -0.297
Metro_vs_SMC 1 3.063 0.0064 0.685
Metro_vs_SMC 2 2.531 0.0203 0.566
Metro_vs_SMC 3 4.466 0.000265 0.999
Metro_vs_SMC 4 3.438 0.00275 0.769
Metro_vs_DEMetro_Z 0 -2.945 0.00831 -0.659
Metro_vs_DEMetro_Z 1 -0.933 0.363 -0.209
Metro_vs_DEMetro_Z 2 -0.256 0.801 -0.057
Metro_vs_DEMetro_Z 3 -1.778 0.0914 -0.398
Metro_vs_DEMetro_Z 4 -1.555 0.137 -0.348
HMC_vs_Metro 0 -1.601 0.126 -0.358
HMC_vs_Metro 1 -1.140 0.268 -0.255
HMC_vs_Metro 2 -3.505 0.00237 -0.784
HMC_vs_Metro 3 -3.623 0.00181 -0.810
HMC_vs_Metro 4 -3.557 0.00211 -0.795
HMC_vs_SMC 0 -3.306 0.00371 -0.739
HMC_vs_SMC 1 2.370 0.0285 0.530
HMC_vs_SMC 2 -2.594 0.0178 -0.580
HMC_vs_SMC 3 0.674 0.508 0.151
HMC_vs_SMC 4 -0.932 0.363 -0.208
DEMetro_Z_vs_SMC 0 1.522 0.145 0.340
DEMetro_Z_vs_SMC 1 3.365 0.00325 0.752
DEMetro_Z_vs_SMC 2 3.577 0.00201 0.800
DEMetro_Z_vs_SMC 3 3.756 0.00134 0.840
DEMetro_Z_vs_SMC 4 4.436 0.000284 0.992
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.066 0.066 0.039 -0.016
HMC 3.0 0.053 0.039 0.023 0.574
HMC 4.0 0.026 0.028 0.014 -0.152
HMC 10.0 0.025 0.026 0.015 -0.110
HMC 50.0 0.017 0.024 0.013 -0.549
SMC 2.1 0.110 0.066 0.039 1.109
SMC 3.0 0.037 0.039 0.023 -0.119
SMC 4.0 0.034 0.028 0.014 0.416
SMC 10.0 0.022 0.026 0.015 -0.298
SMC 50.0 0.019 0.024 0.013 -0.386
Metro 2.1 0.087 0.066 0.039 0.538
Metro 3.0 0.065 0.039 0.023 1.114
Metro 4.0 0.058 0.028 0.014 2.192
Metro 10.0 0.037 0.026 0.015 0.741
Metro 50.0 0.032 0.024 0.013 0.662
DEMetro_Z 2.1 0.145 0.066 0.039 1.999
DEMetro_Z 3.0 0.081 0.039 0.023 1.780
DEMetro_Z 4.0 0.061 0.028 0.014 2.400
DEMetro_Z 10.0 0.050 0.026 0.015 1.595
DEMetro_Z 50.0 0.041 0.024 0.013 1.392
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.219 0.828 -0.061
HMC 3.0 0.599 0.553 0.227
HMC 4.0 -0.847 0.403 -0.227
HMC 10.0 2.358 0.0239 0.839
HMC 50.0 0.819 0.418 0.263
SMC 2.1 1.601 0.119 0.422
SMC 3.0 -0.680 0.501 -0.200
SMC 4.0 -1.337 0.192 -0.335
SMC 10.0 -0.400 0.691 -0.134
SMC 50.0 -1.777 0.0848 -0.477
Metro 2.1 -0.735 0.468 -0.196
Metro 3.0 1.233 0.226 0.521
Metro 4.0 1.576 0.125 0.692
Metro 10.0 4.584 6.08e-05 1.823
Metro 50.0 2.139 0.04 0.877
DEMetro_Z 2.1 -0.475 0.638 -0.127
DEMetro_Z 3.0 3.309 0.00216 1.228
DEMetro_Z 4.0 2.627 0.0124 0.793
DEMetro_Z 10.0 5.582 8.33e-06 3.342
DEMetro_Z 50.0 3.102 0.00368 1.086
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -2.563 0.019 -0.573
HMC_vs_SMC 1 1.508 0.148 0.337
HMC_vs_SMC 2 0.576 0.571 0.129
HMC_vs_SMC 3 3.169 0.00506 0.709
HMC_vs_SMC 4 2.850 0.0102 0.637
Metro_vs_DEMetro_Z 0 -1.364 0.189 -0.305
Metro_vs_DEMetro_Z 1 -1.898 0.073 -0.424
Metro_vs_DEMetro_Z 2 -0.253 0.803 -0.056
Metro_vs_DEMetro_Z 3 -2.292 0.0335 -0.512
Metro_vs_DEMetro_Z 4 -0.484 0.634 -0.108
HMC_vs_Metro 0 1.358 0.19 0.304
HMC_vs_Metro 1 -0.621 0.542 -0.139
HMC_vs_Metro 2 -3.045 0.00666 -0.681
HMC_vs_Metro 3 -2.027 0.0569 -0.453
HMC_vs_Metro 4 -1.339 0.196 -0.299
HMC_vs_DEMetro_Z 0 0.597 0.558 0.133
HMC_vs_DEMetro_Z 1 -2.487 0.0224 -0.556
HMC_vs_DEMetro_Z 2 -3.639 0.00175 -0.814
HMC_vs_DEMetro_Z 3 -4.698 0.000157 -1.051
HMC_vs_DEMetro_Z 4 -1.977 0.0627 -0.442
Metro_vs_SMC 0 -3.309 0.00369 -0.740
Metro_vs_SMC 1 2.152 0.0445 0.481
Metro_vs_SMC 2 2.748 0.0128 0.615
Metro_vs_SMC 3 5.474 2.79e-05 1.224
Metro_vs_SMC 4 3.781 0.00126 0.845
DEMetro_Z_vs_SMC 0 -2.785 0.0118 -0.623
DEMetro_Z_vs_SMC 1 5.466 2.84e-05 1.222
DEMetro_Z_vs_SMC 2 5.405 3.24e-05 1.209
DEMetro_Z_vs_SMC 3 5.961 9.76e-06 1.333
DEMetro_Z_vs_SMC 4 4.717 0.00015 1.055
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 8.387 9.309 15.244 -0.061
HMC 3.0 0.650 0.552 0.433 0.227
HMC 4.0 0.142 0.173 0.139 -0.227
HMC 10.0 0.057 0.040 0.020 0.839
HMC 50.0 0.036 0.031 0.019 0.263
SMC 2.1 15.738 9.309 15.244 0.422
SMC 3.0 0.466 0.552 0.433 -0.200
SMC 4.0 0.127 0.173 0.139 -0.335
SMC 10.0 0.037 0.040 0.020 -0.134
SMC 50.0 0.022 0.031 0.019 -0.477
Metro 2.1 6.327 9.309 15.244 -0.196
Metro 3.0 0.778 0.552 0.433 0.521
Metro 4.0 0.269 0.173 0.139 0.692
Metro 10.0 0.077 0.040 0.020 1.823
Metro 50.0 0.047 0.031 0.019 0.877
DEMetro_Z 2.1 7.372 9.309 15.244 -0.127
DEMetro_Z 3.0 1.084 0.552 0.433 1.228
DEMetro_Z 4.0 0.283 0.173 0.139 0.793
DEMetro_Z 10.0 0.107 0.040 0.020 3.342
DEMetro_Z 50.0 0.051 0.031 0.019 1.086
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.228 0.0346 1.224
HMC 3.0 1.828 0.0794 1.075
HMC 4.0 1.797 0.0821 0.791
HMC 10.0 0.051 0.96 0.015
HMC 50.0 -0.802 0.428 -0.220
SMC 2.1 8.900 2.84e-08 20.527
SMC 3.0 1.513 0.141 0.680
SMC 4.0 0.230 0.82 0.094
SMC 10.0 -1.521 0.138 -0.411
SMC 50.0 -1.491 0.145 -0.402
Metro 2.1 4.573 5.32e-05 1.610
Metro 3.0 5.885 4.9e-06 4.007
Metro 4.0 5.749 9.22e-06 4.966
Metro 10.0 5.678 1.58e-06 1.833
Metro 50.0 3.747 0.000615 1.318
DEMetro_Z 2.1 6.933 2.84e-07 4.132
DEMetro_Z 3.0 7.913 5.97e-08 6.043
DEMetro_Z 4.0 9.405 2.41e-09 6.787
DEMetro_Z 10.0 6.227 1.38e-06 3.477
DEMetro_Z 50.0 5.980 1.12e-06 2.493
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -4.905 9.83e-05 -1.097
Metro_vs_DEMetro_Z 1 -2.044 0.055 -0.457
Metro_vs_DEMetro_Z 2 -1.722 0.101 -0.385
Metro_vs_DEMetro_Z 3 -3.123 0.0056 -0.698
Metro_vs_DEMetro_Z 4 -2.858 0.0101 -0.639
DEMetro_Z_vs_SMC 0 -6.397 3.91e-06 -1.430
DEMetro_Z_vs_SMC 1 6.110 7.12e-06 1.366
DEMetro_Z_vs_SMC 2 7.800 2.43e-07 1.744
DEMetro_Z_vs_SMC 3 7.629 3.37e-07 1.706
DEMetro_Z_vs_SMC 4 7.766 2.6e-07 1.737
HMC_vs_DEMetro_Z 0 -6.609 2.52e-06 -1.478
HMC_vs_DEMetro_Z 1 -4.781 0.00013 -1.069
HMC_vs_DEMetro_Z 2 -7.328 6.02e-07 -1.639
HMC_vs_DEMetro_Z 3 -5.996 9.05e-06 -1.341
HMC_vs_DEMetro_Z 4 -7.224 7.37e-07 -1.615
HMC_vs_Metro 0 -0.693 0.497 -0.155
HMC_vs_Metro 1 -3.460 0.00262 -0.774
HMC_vs_Metro 2 -5.545 2.39e-05 -1.240
HMC_vs_Metro 3 -5.792 1.4e-05 -1.295
HMC_vs_Metro 4 -5.206 5.03e-05 -1.164
HMC_vs_SMC 0 -7.857 2.19e-07 -1.757
HMC_vs_SMC 1 0.559 0.583 0.125
HMC_vs_SMC 2 1.735 0.0989 0.388
HMC_vs_SMC 3 1.634 0.119 0.365
HMC_vs_SMC 4 0.931 0.364 0.208
Metro_vs_SMC 0 -8.079 1.45e-07 -1.806
Metro_vs_SMC 1 4.701 0.000155 1.051
Metro_vs_SMC 2 5.132 5.92e-05 1.148
Metro_vs_SMC 3 10.568 2.15e-09 2.363
Metro_vs_SMC 4 5.574 2.24e-05 1.246
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.170 0.124 0.038 1.224
HMC 3.0 0.085 0.071 0.013 1.075
HMC 4.0 0.056 0.050 0.007 0.791
HMC 10.0 0.037 0.037 0.009 0.015
HMC 50.0 0.030 0.032 0.009 -0.220
SMC 2.1 0.897 0.124 0.038 20.527
SMC 3.0 0.080 0.071 0.013 0.680
SMC 4.0 0.050 0.050 0.007 0.094
SMC 10.0 0.033 0.037 0.009 -0.411
SMC 50.0 0.028 0.032 0.009 -0.402
Metro 2.1 0.185 0.124 0.038 1.610
Metro 3.0 0.122 0.071 0.013 4.007
Metro 4.0 0.086 0.050 0.007 4.966
Metro 10.0 0.054 0.037 0.009 1.833
Metro 50.0 0.044 0.032 0.009 1.318
DEMetro_Z 2.1 0.280 0.124 0.038 4.132
DEMetro_Z 3.0 0.148 0.071 0.013 6.043
DEMetro_Z 4.0 0.099 0.050 0.007 6.787
DEMetro_Z 10.0 0.070 0.037 0.009 3.477
DEMetro_Z 50.0 0.054 0.032 0.009 2.493
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.792 0.088 2.174
HMC 3.0 1.505 0.145 0.920
HMC 4.0 1.305 0.201 0.576
HMC 10.0 0.200 0.842 0.066
HMC 50.0 -0.298 0.767 -0.087
SMC 2.1 11.925 2.39e-10 30.700
SMC 3.0 2.525 0.0181 1.456
SMC 4.0 -0.002 0.999 -0.001
SMC 10.0 -1.114 0.273 -0.314
SMC 50.0 -1.363 0.181 -0.384
Metro 2.1 5.445 1.27e-05 3.410
Metro 3.0 6.566 5.86e-07 3.679
Metro 4.0 5.201 2.18e-05 3.085
Metro 10.0 4.136 0.000196 1.435
Metro 50.0 2.656 0.0118 0.982
DEMetro_Z 2.1 9.830 3.88e-10 5.724
DEMetro_Z 3.0 6.491 1.56e-06 5.323
DEMetro_Z 4.0 5.884 5.87e-06 4.532
DEMetro_Z 10.0 4.891 4.09e-05 2.574
DEMetro_Z 50.0 4.428 0.000122 2.078
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -9.502 1.19e-08 -2.125
DEMetro_Z_vs_SMC 1 3.963 0.000834 0.886
DEMetro_Z_vs_SMC 2 5.353 3.64e-05 1.197
DEMetro_Z_vs_SMC 3 5.915 1.08e-05 1.323
DEMetro_Z_vs_SMC 4 6.017 8.66e-06 1.345
HMC_vs_Metro 0 -0.955 0.351 -0.214
HMC_vs_Metro 1 -3.645 0.00172 -0.815
HMC_vs_Metro 2 -3.770 0.0013 -0.843
HMC_vs_Metro 3 -3.790 0.00124 -0.847
HMC_vs_Metro 4 -3.272 0.00401 -0.732
Metro_vs_DEMetro_Z 0 -3.501 0.00239 -0.783
Metro_vs_DEMetro_Z 1 -1.624 0.121 -0.363
Metro_vs_DEMetro_Z 2 -1.702 0.105 -0.381
Metro_vs_DEMetro_Z 3 -2.271 0.035 -0.508
Metro_vs_DEMetro_Z 4 -2.146 0.045 -0.480
HMC_vs_SMC 0 -8.823 3.8e-08 -1.973
HMC_vs_SMC 1 -0.625 0.539 -0.140
HMC_vs_SMC 2 1.388 0.181 0.310
HMC_vs_SMC 3 1.271 0.219 0.284
HMC_vs_SMC 4 1.177 0.254 0.263
Metro_vs_SMC 0 -10.659 1.87e-09 -2.383
Metro_vs_SMC 1 3.205 0.00466 0.717
Metro_vs_SMC 2 4.563 0.000212 1.020
Metro_vs_SMC 3 6.031 8.41e-06 1.348
Metro_vs_SMC 4 4.302 0.000385 0.962
HMC_vs_DEMetro_Z 0 -2.684 0.0147 -0.600
HMC_vs_DEMetro_Z 1 -4.033 0.000711 -0.902
HMC_vs_DEMetro_Z 2 -4.832 0.000116 -1.081
HMC_vs_DEMetro_Z 3 -4.281 0.000404 -0.957
HMC_vs_DEMetro_Z 4 -4.955 8.8e-05 -1.108
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.025 0.014 0.005 2.174
HMC 3.0 0.018 0.015 0.003 0.920
HMC 4.0 0.017 0.015 0.003 0.576
HMC 10.0 0.015 0.015 0.005 0.066
HMC 50.0 0.014 0.015 0.005 -0.087
SMC 2.1 0.158 0.014 0.005 30.700
SMC 3.0 0.020 0.015 0.003 1.456
SMC 4.0 0.015 0.015 0.003 -0.001
SMC 10.0 0.013 0.015 0.005 -0.314
SMC 50.0 0.013 0.015 0.005 -0.384
Metro 2.1 0.030 0.014 0.005 3.410
Metro 3.0 0.028 0.015 0.003 3.679
Metro 4.0 0.025 0.015 0.003 3.085
Metro 10.0 0.023 0.015 0.005 1.435
Metro 50.0 0.020 0.015 0.005 0.982
DEMetro_Z 2.1 0.041 0.014 0.005 5.724
DEMetro_Z 3.0 0.033 0.015 0.003 5.323
DEMetro_Z 4.0 0.030 0.015 0.003 4.532
DEMetro_Z 10.0 0.029 0.015 0.005 2.574
DEMetro_Z 50.0 0.026 0.015 0.005 2.078
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.680 0.104 -0.420
HMC 3.0 -0.653 0.518 -0.176
HMC 4.0 0.481 0.633 0.146
HMC 10.0 -0.399 0.692 -0.119
HMC 50.0 -1.537 0.133 -0.429
SMC 2.1 1.228 0.227 0.431
SMC 3.0 0.047 0.963 0.013
SMC 4.0 1.094 0.281 0.401
SMC 10.0 -0.083 0.935 -0.022
SMC 50.0 -0.940 0.353 -0.276
Metro 2.1 3.353 0.00228 1.649
Metro 3.0 3.807 0.00058 1.539
Metro 4.0 3.009 0.00584 1.738
Metro 10.0 3.024 0.00486 1.260
Metro 50.0 1.304 0.201 0.479
DEMetro_Z 2.1 4.032 0.000312 1.655
DEMetro_Z 3.0 2.834 0.00818 1.305
DEMetro_Z 4.0 3.431 0.00244 3.046
DEMetro_Z 10.0 3.625 0.000928 1.400
DEMetro_Z 50.0 3.589 0.00119 1.680
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -5.279 4.28e-05 -1.180
HMC_vs_DEMetro_Z 1 -3.289 0.00386 -0.735
HMC_vs_DEMetro_Z 2 -3.254 0.00417 -0.728
HMC_vs_DEMetro_Z 3 -4.879 0.000104 -1.091
HMC_vs_DEMetro_Z 4 -5.055 7.04e-05 -1.130
Metro_vs_SMC 0 2.386 0.0276 0.534
Metro_vs_SMC 1 4.363 0.000335 0.976
Metro_vs_SMC 2 2.317 0.0318 0.518
Metro_vs_SMC 3 3.732 0.00141 0.834
Metro_vs_SMC 4 2.346 0.03 0.525
Metro_vs_DEMetro_Z 0 -0.012 0.991 -0.003
Metro_vs_DEMetro_Z 1 0.476 0.64 0.106
Metro_vs_DEMetro_Z 2 -1.174 0.255 -0.263
Metro_vs_DEMetro_Z 3 -0.322 0.751 -0.072
Metro_vs_DEMetro_Z 4 -3.706 0.0015 -0.829
HMC_vs_Metro 0 -4.687 0.00016 -1.048
HMC_vs_Metro 1 -5.410 3.21e-05 -1.210
HMC_vs_Metro 2 -3.174 0.005 -0.710
HMC_vs_Metro 3 -3.638 0.00175 -0.813
HMC_vs_Metro 4 -2.766 0.0123 -0.619
HMC_vs_SMC 0 -2.902 0.00914 -0.649
HMC_vs_SMC 1 -1.111 0.28 -0.248
HMC_vs_SMC 2 -0.741 0.468 -0.166
HMC_vs_SMC 3 -0.390 0.701 -0.087
HMC_vs_SMC 4 -0.654 0.521 -0.146
DEMetro_Z_vs_SMC 0 2.847 0.0103 0.637
DEMetro_Z_vs_SMC 1 2.850 0.0103 0.637
DEMetro_Z_vs_SMC 2 3.121 0.00562 0.698
DEMetro_Z_vs_SMC 3 4.228 0.000455 0.945
DEMetro_Z_vs_SMC 4 4.573 0.000208 1.023
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.050 0.066 0.039 -0.420
HMC 3.0 0.035 0.039 0.023 -0.176
HMC 4.0 0.030 0.028 0.014 0.146
HMC 10.0 0.025 0.026 0.015 -0.119
HMC 50.0 0.018 0.024 0.013 -0.429
SMC 2.1 0.083 0.066 0.039 0.431
SMC 3.0 0.040 0.039 0.023 0.013
SMC 4.0 0.033 0.028 0.014 0.401
SMC 10.0 0.026 0.026 0.015 -0.022
SMC 50.0 0.020 0.024 0.013 -0.276
Metro 2.1 0.131 0.066 0.039 1.649
Metro 3.0 0.075 0.039 0.023 1.539
Metro 4.0 0.052 0.028 0.014 1.738
Metro 10.0 0.045 0.026 0.015 1.260
Metro 50.0 0.030 0.024 0.013 0.479
DEMetro_Z 2.1 0.131 0.066 0.039 1.655
DEMetro_Z 3.0 0.070 0.039 0.023 1.305
DEMetro_Z 4.0 0.070 0.028 0.014 3.046
DEMetro_Z 10.0 0.047 0.026 0.015 1.400
DEMetro_Z 50.0 0.045 0.024 0.013 1.680
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.809 0.425 -0.214
HMC 3.0 0.061 0.952 0.019
HMC 4.0 0.362 0.72 0.120
HMC 10.0 0.048 0.962 0.017
HMC 50.0 1.061 0.296 0.368
SMC 2.1 -0.168 0.868 -0.044
SMC 3.0 -0.400 0.692 -0.118
SMC 4.0 -1.175 0.25 -0.294
SMC 10.0 0.381 0.705 0.139
SMC 50.0 -0.699 0.49 -0.184
Metro 2.1 -0.718 0.478 -0.188
Metro 3.0 1.564 0.126 0.553
Metro 4.0 1.972 0.0561 0.675
Metro 10.0 3.741 0.000875 1.967
Metro 50.0 3.520 0.00118 1.260
DEMetro_Z 2.1 -0.635 0.529 -0.171
DEMetro_Z 3.0 1.188 0.243 0.346
DEMetro_Z 4.0 1.917 0.0691 2.003
DEMetro_Z 10.0 4.691 7.98e-05 2.722
DEMetro_Z 50.0 4.054 0.000342 1.906
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -2.278 0.0344 -0.509
HMC_vs_SMC 1 0.763 0.455 0.171
HMC_vs_SMC 2 1.591 0.128 0.356
HMC_vs_SMC 3 -0.324 0.749 -0.073
HMC_vs_SMC 4 1.967 0.064 0.440
Metro_vs_DEMetro_Z 0 -0.547 0.59 -0.122
Metro_vs_DEMetro_Z 1 0.900 0.379 0.201
Metro_vs_DEMetro_Z 2 -1.234 0.232 -0.276
Metro_vs_DEMetro_Z 3 -1.017 0.322 -0.227
Metro_vs_DEMetro_Z 4 -1.455 0.162 -0.325
HMC_vs_Metro 0 -0.704 0.49 -0.157
HMC_vs_Metro 1 -3.032 0.00686 -0.678
HMC_vs_Metro 2 -1.556 0.136 -0.348
HMC_vs_Metro 3 -3.409 0.00294 -0.762
HMC_vs_Metro 4 -2.109 0.0484 -0.472
HMC_vs_DEMetro_Z 0 -1.355 0.191 -0.303
HMC_vs_DEMetro_Z 1 -1.703 0.105 -0.381
HMC_vs_DEMetro_Z 2 -1.739 0.0983 -0.389
HMC_vs_DEMetro_Z 3 -5.017 7.65e-05 -1.122
HMC_vs_DEMetro_Z 4 -2.746 0.0128 -0.614
Metro_vs_SMC 0 -2.178 0.0422 -0.487
Metro_vs_SMC 1 3.136 0.00544 0.701
Metro_vs_SMC 2 4.915 9.61e-05 1.099
Metro_vs_SMC 3 3.101 0.00588 0.694
Metro_vs_SMC 4 4.032 0.000713 0.902
DEMetro_Z_vs_SMC 0 -1.587 0.129 -0.355
DEMetro_Z_vs_SMC 1 2.449 0.0242 0.548
DEMetro_Z_vs_SMC 2 2.249 0.0366 0.503
DEMetro_Z_vs_SMC 3 3.654 0.00169 0.817
DEMetro_Z_vs_SMC 4 4.616 0.000188 1.032
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.041 9.309 15.244 -0.214
HMC 3.0 0.560 0.552 0.433 0.019
HMC 4.0 0.190 0.173 0.139 0.120
HMC 10.0 0.040 0.040 0.020 0.017
HMC 50.0 0.038 0.031 0.019 0.368
SMC 2.1 8.644 9.309 15.244 -0.044
SMC 3.0 0.501 0.552 0.433 -0.118
SMC 4.0 0.132 0.173 0.139 -0.294
SMC 10.0 0.043 0.040 0.020 0.139
SMC 50.0 0.028 0.031 0.019 -0.184
Metro 2.1 6.440 9.309 15.244 -0.188
Metro 3.0 0.792 0.552 0.433 0.553
Metro 4.0 0.267 0.173 0.139 0.675
Metro 10.0 0.080 0.040 0.020 1.967
Metro 50.0 0.055 0.031 0.019 1.260
DEMetro_Z 2.1 6.701 9.309 15.244 -0.171
DEMetro_Z 3.0 0.702 0.552 0.433 0.346
DEMetro_Z 4.0 0.451 0.173 0.139 2.003
DEMetro_Z 10.0 0.095 0.040 0.020 2.722
DEMetro_Z 50.0 0.067 0.031 0.019 1.906
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.159 0.254 0.420
HMC 3.0 0.876 0.388 0.364
HMC 4.0 1.045 0.304 0.436
HMC 10.0 0.147 0.884 0.044
HMC 50.0 -0.560 0.579 -0.154
SMC 2.1 6.905 1.05e-06 9.675
SMC 3.0 0.542 0.592 0.223
SMC 4.0 0.180 0.858 0.063
SMC 10.0 -0.344 0.733 -0.100
SMC 50.0 -1.110 0.275 -0.306
Metro 2.1 7.308 3.57e-08 3.267
Metro 3.0 7.687 4.04e-08 4.387
Metro 4.0 6.728 6.76e-07 4.668
Metro 10.0 5.387 8.28e-06 2.511
Metro 50.0 4.378 9.09e-05 1.408
DEMetro_Z 2.1 9.746 1.25e-11 3.535
DEMetro_Z 3.0 7.915 2.13e-08 4.403
DEMetro_Z 4.0 6.275 3.76e-06 7.838
DEMetro_Z 10.0 6.875 1.08e-07 3.025
DEMetro_Z 50.0 6.077 1.33e-06 2.914
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.657 0.519 -0.147
Metro_vs_DEMetro_Z 1 -0.028 0.978 -0.006
Metro_vs_DEMetro_Z 2 -2.009 0.059 -0.449
Metro_vs_DEMetro_Z 3 -0.970 0.344 -0.217
Metro_vs_DEMetro_Z 4 -4.604 0.000194 -1.029
DEMetro_Z_vs_SMC 0 -4.044 0.000693 -0.904
DEMetro_Z_vs_SMC 1 7.685 3.03e-07 1.719
DEMetro_Z_vs_SMC 2 6.682 2.17e-06 1.494
DEMetro_Z_vs_SMC 3 8.435 7.56e-08 1.886
DEMetro_Z_vs_SMC 4 7.377 5.47e-07 1.650
HMC_vs_DEMetro_Z 0 -11.854 3.19e-10 -2.651
HMC_vs_DEMetro_Z 1 -5.835 1.28e-05 -1.305
HMC_vs_DEMetro_Z 2 -5.370 3.5e-05 -1.201
HMC_vs_DEMetro_Z 3 -8.953 3.03e-08 -2.002
HMC_vs_DEMetro_Z 4 -6.282 4.96e-06 -1.405
HMC_vs_Metro 0 -6.477 3.31e-06 -1.448
HMC_vs_Metro 1 -6.692 2.13e-06 -1.496
HMC_vs_Metro 2 -5.980 9.37e-06 -1.337
HMC_vs_Metro 3 -5.372 3.49e-05 -1.201
HMC_vs_Metro 4 -4.868 0.000107 -1.088
HMC_vs_SMC 0 -6.294 4.84e-06 -1.407
HMC_vs_SMC 1 0.387 0.703 0.087
HMC_vs_SMC 2 0.892 0.384 0.199
HMC_vs_SMC 3 0.520 0.609 0.116
HMC_vs_SMC 4 0.599 0.556 0.134
Metro_vs_SMC 0 -4.600 0.000195 -1.029
Metro_vs_SMC 1 6.754 1.88e-06 1.510
Metro_vs_SMC 2 6.260 5.19e-06 1.400
Metro_vs_SMC 3 6.270 5.09e-06 1.402
Metro_vs_SMC 4 7.079 9.8e-07 1.583
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.140 0.124 0.038 0.420
HMC 3.0 0.076 0.071 0.013 0.364
HMC 4.0 0.053 0.050 0.007 0.436
HMC 10.0 0.037 0.037 0.009 0.044
HMC 50.0 0.030 0.032 0.009 -0.154
SMC 2.1 0.488 0.124 0.038 9.675
SMC 3.0 0.074 0.071 0.013 0.223
SMC 4.0 0.050 0.050 0.007 0.063
SMC 10.0 0.036 0.037 0.009 -0.100
SMC 50.0 0.029 0.032 0.009 -0.306
Metro 2.1 0.247 0.124 0.038 3.267
Metro 3.0 0.127 0.071 0.013 4.387
Metro 4.0 0.084 0.050 0.007 4.668
Metro 10.0 0.061 0.037 0.009 2.511
Metro 50.0 0.044 0.032 0.009 1.408
DEMetro_Z 2.1 0.257 0.124 0.038 3.535
DEMetro_Z 3.0 0.127 0.071 0.013 4.403
DEMetro_Z 4.0 0.107 0.050 0.007 7.838
DEMetro_Z 10.0 0.066 0.037 0.009 3.025
DEMetro_Z 50.0 0.058 0.032 0.009 2.914
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.373 0.0233 0.907
HMC 3.0 1.255 0.219 0.537
HMC 4.0 -0.656 0.516 -0.244
HMC 10.0 0.887 0.381 0.281
HMC 50.0 -0.025 0.98 -0.007
SMC 2.1 9.088 1.97e-08 18.929
SMC 3.0 1.290 0.209 0.768
SMC 4.0 -0.612 0.544 -0.193
SMC 10.0 0.058 0.954 0.018
SMC 50.0 -0.610 0.546 -0.173
Metro 2.1 9.865 8.4e-11 4.648
Metro 3.0 6.839 5.1e-07 4.697
Metro 4.0 6.821 2.14e-07 3.430
Metro 10.0 4.816 4.34e-05 2.320
Metro 50.0 4.081 0.000222 1.283
DEMetro_Z 2.1 7.608 9.15e-08 5.286
DEMetro_Z 3.0 6.893 3.89e-07 4.449
DEMetro_Z 4.0 7.801 4.1e-08 4.805
DEMetro_Z 10.0 5.143 1.69e-05 2.431
DEMetro_Z 50.0 4.733 5.36e-05 2.258
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -6.050 8.08e-06 -1.353
DEMetro_Z_vs_SMC 1 4.983 8.25e-05 1.114
DEMetro_Z_vs_SMC 2 7.663 3.16e-07 1.714
DEMetro_Z_vs_SMC 3 6.434 3.61e-06 1.439
DEMetro_Z_vs_SMC 4 5.422 3.12e-05 1.212
HMC_vs_Metro 0 -6.330 4.49e-06 -1.415
HMC_vs_Metro 1 -6.762 1.85e-06 -1.512
HMC_vs_Metro 2 -6.999 1.15e-06 -1.565
HMC_vs_Metro 3 -4.163 0.000528 -0.931
HMC_vs_Metro 4 -3.777 0.00127 -0.845
Metro_vs_DEMetro_Z 0 -0.875 0.392 -0.196
Metro_vs_DEMetro_Z 1 0.276 0.786 0.062
Metro_vs_DEMetro_Z 2 -1.605 0.125 -0.359
Metro_vs_DEMetro_Z 3 -0.199 0.845 -0.044
Metro_vs_DEMetro_Z 4 -2.817 0.011 -0.630
HMC_vs_SMC 0 -8.826 3.78e-08 -1.973
HMC_vs_SMC 1 -0.371 0.715 -0.083
HMC_vs_SMC 2 -0.136 0.893 -0.030
HMC_vs_SMC 3 0.919 0.369 0.206
HMC_vs_SMC 4 0.558 0.583 0.125
Metro_vs_SMC 0 -7.225 7.35e-07 -1.616
Metro_vs_SMC 1 4.608 0.000192 1.030
Metro_vs_SMC 2 7.674 3.09e-07 1.716
Metro_vs_SMC 3 5.262 4.45e-05 1.177
Metro_vs_SMC 4 6.063 7.86e-06 1.356
HMC_vs_DEMetro_Z 0 -6.904 1.39e-06 -1.544
HMC_vs_DEMetro_Z 1 -5.490 2.7e-05 -1.228
HMC_vs_DEMetro_Z 2 -6.644 2.35e-06 -1.486
HMC_vs_DEMetro_Z 3 -5.573 2.25e-05 -1.246
HMC_vs_DEMetro_Z 4 -4.480 0.000257 -1.002
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.019 0.014 0.005 0.907
HMC 3.0 0.017 0.015 0.003 0.537
HMC 4.0 0.014 0.015 0.003 -0.244
HMC 10.0 0.016 0.015 0.005 0.281
HMC 50.0 0.015 0.015 0.005 -0.007
SMC 2.1 0.103 0.014 0.005 18.929
SMC 3.0 0.018 0.015 0.003 0.768
SMC 4.0 0.014 0.015 0.003 -0.193
SMC 10.0 0.015 0.015 0.005 0.018
SMC 50.0 0.014 0.015 0.005 -0.173
Metro 2.1 0.036 0.014 0.005 4.648
Metro 3.0 0.031 0.015 0.003 4.697
Metro 4.0 0.026 0.015 0.003 3.430
Metro 10.0 0.027 0.015 0.005 2.320
Metro 50.0 0.022 0.015 0.005 1.283
DEMetro_Z 2.1 0.039 0.014 0.005 5.286
DEMetro_Z 3.0 0.030 0.015 0.003 4.449
DEMetro_Z 4.0 0.031 0.015 0.003 4.805
DEMetro_Z 10.0 0.028 0.015 0.005 2.431
DEMetro_Z 50.0 0.027 0.015 0.005 2.258
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Varying_Tails_with_high_Dimension (MvStudentT, nu, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.543 0.139 5.596
HMC 3.0 2.107 0.0486 10.613
HMC 4.0 0.384 0.704 0.285
HMC 10.0 -1.924 0.0626 -0.530
HMC 50.0 -3.176 0.00309 -0.890
SMC 2.1 32.386 2.31e-18 70.188
SMC 3.0 31.204 7.07e-18 116.418
SMC 4.0 29.005 2.44e-17 84.083
SMC 10.0 24.766 3.36e-16 48.880
SMC 50.0 21.251 6.14e-16 18.941
Metro 2.1 4.122 0.000571 13.866
Metro 3.0 11.409 1.8e-10 11.291
Metro 4.0 16.730 2.94e-15 9.671
Metro 10.0 15.079 2.3e-15 7.046
Metro 50.0 14.552 5.3e-16 5.815
DEMetro_Z 2.1 17.660 3e-13 335.130
DEMetro_Z 3.0 20.961 1.35e-14 620.466
DEMetro_Z 4.0 16.329 1.22e-12 473.692
DEMetro_Z 10.0 23.729 1.36e-15 243.476
DEMetro_Z 50.0 11.683 4.06e-10 288.577
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -16.661 8.56e-13 -3.726
HMC_vs_DEMetro_Z 1 -20.612 1.84e-14 -4.609
HMC_vs_DEMetro_Z 2 -16.218 1.38e-12 -3.626
HMC_vs_DEMetro_Z 3 -23.693 1.43e-15 -5.298
HMC_vs_DEMetro_Z 4 -11.712 3.9e-10 -2.619
Metro_vs_SMC 0 -14.427 1.09e-11 -3.226
Metro_vs_SMC 1 -26.492 1.82e-16 -5.924
Metro_vs_SMC 2 -25.728 3.13e-16 -5.753
Metro_vs_SMC 3 -21.373 9.5e-15 -4.779
Metro_vs_SMC 4 -14.869 6.42e-12 -3.325
Metro_vs_DEMetro_Z 0 -16.466 1.06e-12 -3.682
Metro_vs_DEMetro_Z 1 -20.446 2.13e-14 -4.572
Metro_vs_DEMetro_Z 2 -16.035 1.69e-12 -3.586
Metro_vs_DEMetro_Z 3 -22.922 2.63e-15 -5.126
Metro_vs_DEMetro_Z 4 -11.458 5.63e-10 -2.562
HMC_vs_Metro 0 -1.571 0.133 -0.351
HMC_vs_Metro 1 -0.134 0.895 -0.030
HMC_vs_Metro 2 -11.130 9.14e-10 -2.489
HMC_vs_Metro 3 -15.918 1.93e-12 -3.559
HMC_vs_Metro 4 -16.223 1.38e-12 -3.628
HMC_vs_SMC 0 -18.241 1.69e-13 -4.079
HMC_vs_SMC 1 -17.115 5.3e-13 -3.827
HMC_vs_SMC 2 -25.181 4.66e-16 -5.631
HMC_vs_SMC 3 -25.282 4.33e-16 -5.653
HMC_vs_SMC 4 -23.140 2.21e-15 -5.174
DEMetro_Z_vs_SMC 0 13.954 1.95e-11 3.120
DEMetro_Z_vs_SMC 1 17.262 4.55e-13 3.860
DEMetro_Z_vs_SMC 2 13.553 3.23e-11 3.031
DEMetro_Z_vs_SMC 3 18.241 1.69e-13 4.079
DEMetro_Z_vs_SMC 4 10.781 1.55e-09 2.411
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.191 0.068 0.022 5.596
HMC 3.0 0.080 0.036 0.004 10.613
HMC 4.0 0.033 0.032 0.003 0.285
HMC 10.0 0.022 0.024 0.004 -0.530
HMC 50.0 0.019 0.022 0.003 -0.890
SMC 2.1 1.612 0.068 0.022 70.188
SMC 3.0 0.521 0.036 0.004 116.418
SMC 4.0 0.320 0.032 0.003 84.083
SMC 10.0 0.203 0.024 0.004 48.880
SMC 50.0 0.083 0.022 0.003 18.941
Metro 2.1 0.373 0.068 0.022 13.866
Metro 3.0 0.083 0.036 0.004 11.291
Metro 4.0 0.065 0.032 0.003 9.671
Metro 10.0 0.050 0.024 0.004 7.046
Metro 50.0 0.041 0.022 0.003 5.815
DEMetro_Z 2.1 7.438 0.068 0.022 335.130
DEMetro_Z 3.0 2.619 0.036 0.004 620.466
DEMetro_Z 4.0 1.658 0.032 0.003 473.692
DEMetro_Z 10.0 0.916 0.024 0.004 243.476
DEMetro_Z 50.0 0.955 0.022 0.003 288.577
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.126 0.272 0.879
HMC 3.0 2.196 0.0348 0.822
HMC 4.0 2.710 0.0132 2.943
HMC 10.0 5.035 5.15e-05 4.510
HMC 50.0 7.131 4.55e-08 3.031
SMC 2.1 164.278 5.83e-34 169.471
SMC 3.0 126.843 2.42e-29 838.185
SMC 4.0 170.240 1.02e-31 3897.980
SMC 10.0 87.339 3.25e-26 15438.243
SMC 50.0 37.079 3.44e-19 1395.231
Metro 2.1 1.869 0.0766 3.343
Metro 3.0 2.628 0.0128 1.025
Metro 4.0 4.373 0.000292 5.900
Metro 10.0 11.569 1.41e-10 11.515
Metro 50.0 17.271 1.05e-17 7.319
DEMetro_Z 2.1 11.391 5.77e-10 45.665
DEMetro_Z 3.0 10.811 1.47e-09 181.266
DEMetro_Z 4.0 12.091 2.28e-10 797.399
DEMetro_Z 10.0 15.911 1.94e-12 1687.856
DEMetro_Z 50.0 6.439 3.58e-06 1859.398
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -148.273 1.42e-30 -33.155
HMC_vs_SMC 1 -124.376 3.98e-29 -27.811
HMC_vs_SMC 2 -168.781 1.21e-31 -37.741
HMC_vs_SMC 3 -87.315 3.27e-26 -19.524
HMC_vs_SMC 4 -37.019 3.56e-19 -8.278
Metro_vs_DEMetro_Z 0 -9.407 1.4e-08 -2.103
Metro_vs_DEMetro_Z 1 -10.822 1.45e-09 -2.420
Metro_vs_DEMetro_Z 2 -11.925 2.88e-10 -2.667
Metro_vs_DEMetro_Z 3 -15.781 2.25e-12 -3.529
Metro_vs_DEMetro_Z 4 -6.412 3.78e-06 -1.434
HMC_vs_Metro 0 -1.278 0.217 -0.286
HMC_vs_Metro 1 -0.658 0.519 -0.147
HMC_vs_Metro 2 -1.488 0.153 -0.333
HMC_vs_Metro 3 -5.260 4.47e-05 -1.176
HMC_vs_Metro 4 -8.480 6.98e-08 -1.896
HMC_vs_DEMetro_Z 0 -11.088 9.73e-10 -2.479
HMC_vs_DEMetro_Z 1 -10.784 1.54e-09 -2.411
HMC_vs_DEMetro_Z 2 -12.082 2.31e-10 -2.702
HMC_vs_DEMetro_Z 3 -15.888 1.99e-12 -3.553
HMC_vs_DEMetro_Z 4 -6.427 3.67e-06 -1.437
Metro_vs_SMC 0 -81.474 1.21e-25 -18.218
Metro_vs_SMC 1 -126.671 2.82e-29 -28.324
Metro_vs_SMC 2 -170.707 9.76e-32 -38.171
Metro_vs_SMC 3 -87.451 3.17e-26 -19.555
Metro_vs_SMC 4 -36.923 3.73e-19 -8.256
DEMetro_Z_vs_SMC 0 -29.188 3.02e-17 -6.527
DEMetro_Z_vs_SMC 1 -34.629 1.24e-18 -7.743
DEMetro_Z_vs_SMC 2 -44.056 1.35e-20 -9.851
DEMetro_Z_vs_SMC 3 -59.121 5.26e-23 -13.220
DEMetro_Z_vs_SMC 4 1.575 0.132 0.352
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 24.049 8.319 17.897 0.879
HMC 3.0 1.044 0.639 0.493 0.822
HMC 4.0 0.304 0.164 0.047 2.943
HMC 10.0 0.074 0.048 0.006 4.510
HMC 50.0 0.047 0.033 0.005 3.031
SMC 2.1 3041.344 8.319 17.897 169.471
SMC 3.0 414.083 0.639 0.493 838.185
SMC 4.0 184.440 0.164 0.047 3897.980
SMC 10.0 88.051 0.048 0.006 15438.243
SMC 50.0 6.432 0.033 0.005 1395.231
Metro 2.1 68.147 8.319 17.897 3.343
Metro 3.0 1.144 0.639 0.493 1.025
Metro 4.0 0.443 0.164 0.047 5.900
Metro 10.0 0.114 0.048 0.006 11.515
Metro 50.0 0.067 0.033 0.005 7.319
DEMetro_Z 2.1 825.584 8.319 17.897 45.665
DEMetro_Z 3.0 90.050 0.639 0.493 181.266
DEMetro_Z 4.0 37.861 0.164 0.047 797.399
DEMetro_Z 10.0 9.670 0.048 0.006 1687.856
DEMetro_Z 50.0 8.560 0.033 0.005 1859.398
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.812 0.0111 13.971
HMC 3.0 4.036 0.000702 21.890
HMC 4.0 3.839 0.00107 8.590
HMC 10.0 3.302 0.00241 1.428
HMC 50.0 0.301 0.765 0.084
SMC 2.1 325.240 3.35e-37 1509.402
SMC 3.0 240.106 1.45e-34 3248.487
SMC 4.0 303.155 1.7e-36 3500.432
SMC 10.0 152.825 7.85e-31 2903.634
SMC 50.0 54.552 2.35e-22 718.094
Metro 2.1 3.779 0.00127 75.782
Metro 3.0 6.215 5.56e-06 25.623
Metro 4.0 8.680 4.28e-08 21.265
Metro 10.0 15.236 1.21e-13 10.500
Metro 50.0 17.599 1.09e-17 7.683
DEMetro_Z 2.1 23.365 1.85e-15 724.848
DEMetro_Z 3.0 21.104 1.2e-14 1315.486
DEMetro_Z 4.0 21.283 1.02e-14 1309.606
DEMetro_Z 10.0 24.751 6.39e-16 733.131
DEMetro_Z 50.0 13.084 5.93e-11 697.978
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -16.957 6.25e-13 -3.792
Metro_vs_DEMetro_Z 1 -21.028 1.28e-14 -4.702
Metro_vs_DEMetro_Z 2 -20.763 1.61e-14 -4.643
Metro_vs_DEMetro_Z 3 -24.206 9.66e-16 -5.413
Metro_vs_DEMetro_Z 4 -12.955 7.04e-11 -2.897
DEMetro_Z_vs_SMC 0 -25.225 4.52e-16 -5.640
DEMetro_Z_vs_SMC 1 -29.856 1.98e-17 -6.676
DEMetro_Z_vs_SMC 2 -35.206 9.11e-19 -7.872
DEMetro_Z_vs_SMC 3 -53.489 3.48e-22 -11.960
DEMetro_Z_vs_SMC 4 -0.363 0.72 -0.081
HMC_vs_DEMetro_Z 0 -22.154 4.92e-15 -4.954
HMC_vs_DEMetro_Z 1 -20.608 1.85e-14 -4.608
HMC_vs_DEMetro_Z 2 -21.266 1.04e-14 -4.755
HMC_vs_DEMetro_Z 3 -24.721 6.55e-16 -5.528
HMC_vs_DEMetro_Z 4 -13.082 5.95e-11 -2.925
HMC_vs_Metro 0 -2.930 0.0086 -0.655
HMC_vs_Metro 1 -0.494 0.627 -0.111
HMC_vs_Metro 2 -3.489 0.00246 -0.780
HMC_vs_Metro 3 -10.955 1.19e-09 -2.450
HMC_vs_Metro 4 -17.254 4.58e-13 -3.858
HMC_vs_SMC 0 -279.953 8.12e-36 -62.599
HMC_vs_SMC 1 -206.822 2.55e-33 -46.247
HMC_vs_SMC 2 -275.556 1.1e-35 -61.616
HMC_vs_SMC 3 -153.056 7.76e-31 -34.224
HMC_vs_SMC 4 -54.486 2.46e-22 -12.183
Metro_vs_SMC 0 -67.620 4.14e-24 -15.120
Metro_vs_SMC 1 -236.867 1.94e-34 -52.965
Metro_vs_SMC 2 -292.874 3.45e-36 -65.489
Metro_vs_SMC 3 -154.995 6.11e-31 -34.658
Metro_vs_SMC 4 -54.083 2.83e-22 -12.093
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.508 0.116 0.028 13.971
HMC 3.0 0.165 0.064 0.005 21.890
HMC 4.0 0.073 0.049 0.003 8.590
HMC 10.0 0.037 0.033 0.002 1.428
HMC 50.0 0.029 0.029 0.002 0.084
SMC 2.1 42.456 0.116 0.028 1509.402
SMC 3.0 15.109 0.064 0.005 3248.487
SMC 4.0 9.873 0.049 0.003 3500.432
SMC 10.0 6.673 0.033 0.002 2903.634
SMC 50.0 1.372 0.029 0.002 718.094
Metro 2.1 2.242 0.116 0.028 75.782
Metro 3.0 0.183 0.064 0.005 25.623
Metro 4.0 0.109 0.049 0.003 21.265
Metro 10.0 0.057 0.033 0.002 10.500
Metro 50.0 0.044 0.029 0.002 7.683
DEMetro_Z 2.1 20.449 0.116 0.028 724.848
DEMetro_Z 3.0 6.157 0.064 0.005 1315.486
DEMetro_Z 4.0 3.724 0.049 0.003 1309.606
DEMetro_Z 10.0 1.710 0.033 0.002 733.131
DEMetro_Z 50.0 1.335 0.029 0.002 697.978
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.850 0.00108 33.541
HMC 3.0 3.544 0.00216 18.023
HMC 4.0 3.581 0.00191 6.386
HMC 10.0 2.264 0.0298 0.831
HMC 50.0 0.273 0.786 0.074
SMC 2.1 185.579 3.5e-34 233.263
SMC 3.0 201.688 4.8e-36 200.189
SMC 4.0 228.943 1.16e-35 320.057
SMC 10.0 158.971 2.87e-32 243.404
SMC 50.0 98.555 7.63e-28 183.843
Metro 2.1 8.292 9.76e-08 128.001
Metro 3.0 6.825 1.53e-06 20.701
Metro 4.0 10.131 3.3e-09 20.001
Metro 10.0 15.744 1.07e-14 9.000
Metro 50.0 15.366 2.77e-16 6.489
DEMetro_Z 2.1 67.117 3.73e-24 280.817
DEMetro_Z 3.0 64.571 7.19e-24 234.678
DEMetro_Z 4.0 63.357 1.24e-23 350.890
DEMetro_Z 10.0 54.478 2.02e-22 243.097
DEMetro_Z 50.0 31.604 6.5e-18 232.913
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 12.201 1.96e-10 2.728
DEMetro_Z_vs_SMC 1 8.899 3.33e-08 1.990
DEMetro_Z_vs_SMC 2 5.429 3.08e-05 1.214
DEMetro_Z_vs_SMC 3 -0.070 0.945 -0.016
DEMetro_Z_vs_SMC 4 6.838 1.59e-06 1.529
HMC_vs_Metro 0 -4.665 0.000169 -1.043
HMC_vs_Metro 1 -0.416 0.682 -0.093
HMC_vs_Metro 2 -4.942 9.05e-05 -1.105
HMC_vs_Metro 3 -11.469 5.54e-10 -2.565
HMC_vs_Metro 4 -15.708 2.44e-12 -3.512
Metro_vs_DEMetro_Z 0 -10.238 3.6e-09 -2.289
Metro_vs_DEMetro_Z 1 -46.011 5.96e-21 -10.288
Metro_vs_DEMetro_Z 2 -51.548 7e-22 -11.526
Metro_vs_DEMetro_Z 3 -50.106 1.2e-21 -11.204
Metro_vs_DEMetro_Z 4 -30.435 1.38e-17 -6.805
HMC_vs_SMC 0 -22.111 5.1e-15 -4.944
HMC_vs_SMC 1 -35.814 6.61e-19 -8.008
HMC_vs_SMC 2 -146.927 1.68e-30 -32.854
HMC_vs_SMC 3 -166.633 1.54e-31 -37.260
HMC_vs_SMC 4 -96.538 4.87e-27 -21.587
Metro_vs_SMC 0 -6.992 1.17e-06 -1.563
Metro_vs_SMC 1 -50.081 1.21e-21 -11.199
Metro_vs_SMC 2 -124.286 4.04e-29 -27.791
Metro_vs_SMC 3 -142.136 3.16e-30 -31.782
Metro_vs_SMC 4 -94.337 7.55e-27 -21.094
HMC_vs_DEMetro_Z 0 -22.560 3.53e-15 -5.045
HMC_vs_DEMetro_Z 1 -41.357 4.44e-20 -9.248
HMC_vs_DEMetro_Z 2 -60.866 3.03e-23 -13.610
HMC_vs_DEMetro_Z 3 -54.726 2.26e-22 -12.237
HMC_vs_DEMetro_Z 4 -31.619 6.79e-18 -7.070
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.071 0.015 0.002 33.541
HMC 3.0 0.050 0.015 0.002 18.023
HMC 4.0 0.023 0.015 0.001 6.386
HMC 10.0 0.015 0.014 0.002 0.831
HMC 50.0 0.014 0.014 0.002 0.074
SMC 2.1 0.407 0.015 0.002 233.263
SMC 3.0 0.406 0.015 0.002 200.189
SMC 4.0 0.402 0.015 0.001 320.057
SMC 10.0 0.398 0.014 0.002 243.404
SMC 50.0 0.306 0.014 0.002 183.843
Metro 2.1 0.230 0.015 0.002 128.001
Metro 3.0 0.055 0.015 0.002 20.701
Metro 4.0 0.039 0.015 0.001 20.001
Metro 10.0 0.028 0.014 0.002 9.000
Metro 50.0 0.024 0.014 0.002 6.489
DEMetro_Z 2.1 0.487 0.015 0.002 280.817
DEMetro_Z 3.0 0.474 0.015 0.002 234.678
DEMetro_Z 4.0 0.440 0.015 0.001 350.890
DEMetro_Z 10.0 0.398 0.014 0.002 243.097
DEMetro_Z 50.0 0.384 0.014 0.002 232.913
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.256 0.223 1.608
HMC 3.0 1.593 0.128 12.694
HMC 4.0 0.984 0.337 7.860
HMC 10.0 -2.783 0.00867 -0.767
HMC 50.0 -3.183 0.00292 -1.059
SMC 2.1 27.180 6.75e-17 61.285
SMC 3.0 23.788 1.2e-15 112.294
SMC 4.0 19.681 3.76e-14 79.628
SMC 10.0 22.719 1.52e-15 40.914
SMC 50.0 12.275 8.29e-11 16.049
Metro 2.1 5.018 6.9e-05 8.376
Metro 3.0 12.910 2.06e-11 13.368
Metro 4.0 13.545 1.96e-12 9.814
Metro 10.0 14.241 1.81e-14 6.948
Metro 50.0 12.041 1.48e-12 6.048
DEMetro_Z 2.1 20.287 2.44e-14 337.269
DEMetro_Z 3.0 17.084 5.46e-13 600.693
DEMetro_Z 4.0 16.245 1.34e-12 381.502
DEMetro_Z 10.0 19.854 3.6e-14 273.200
DEMetro_Z 50.0 12.648 1.05e-10 166.381
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -20.103 2.9e-14 -4.495
HMC_vs_DEMetro_Z 1 -15.057 5.15e-12 -3.367
HMC_vs_DEMetro_Z 2 -14.453 1.06e-11 -3.232
HMC_vs_DEMetro_Z 3 -19.951 3.33e-14 -4.461
HMC_vs_DEMetro_Z 4 -12.680 1.02e-10 -2.835
Metro_vs_SMC 0 -19.248 6.38e-14 -4.304
Metro_vs_SMC 1 -18.715 1.06e-13 -4.185
Metro_vs_SMC 2 -16.548 9.66e-13 -3.700
Metro_vs_SMC 3 -18.536 1.26e-13 -4.145
Metro_vs_SMC 4 -7.140 8.69e-07 -1.597
Metro_vs_DEMetro_Z 0 -19.870 3.58e-14 -4.443
Metro_vs_DEMetro_Z 1 -16.873 6.83e-13 -3.773
Metro_vs_DEMetro_Z 2 -15.741 2.35e-12 -3.520
Metro_vs_DEMetro_Z 3 -19.484 5.12e-14 -4.357
Metro_vs_DEMetro_Z 4 -12.095 2.27e-10 -2.704
HMC_vs_Metro 0 -3.139 0.00541 -0.702
HMC_vs_Metro 1 -0.081 0.936 -0.018
HMC_vs_Metro 2 -0.245 0.809 -0.055
HMC_vs_Metro 3 -16.945 6.33e-13 -3.789
HMC_vs_Metro 4 -14.892 6.25e-12 -3.330
HMC_vs_SMC 0 -22.275 4.45e-15 -4.981
HMC_vs_SMC 1 -12.285 1.74e-10 -2.747
HMC_vs_SMC 2 -8.946 3.07e-08 -2.000
HMC_vs_SMC 3 -23.107 2.27e-15 -5.167
HMC_vs_SMC 4 -13.276 4.61e-11 -2.969
DEMetro_Z_vs_SMC 0 16.533 9.82e-13 3.697
DEMetro_Z_vs_SMC 1 13.431 3.78e-11 3.003
DEMetro_Z_vs_SMC 2 12.248 1.83e-10 2.739
DEMetro_Z_vs_SMC 3 16.824 7.19e-13 3.762
DEMetro_Z_vs_SMC 4 11.200 8.24e-10 2.504
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.103 0.068 0.022 1.608
HMC 3.0 0.089 0.036 0.004 12.694
HMC 4.0 0.059 0.032 0.003 7.860
HMC 10.0 0.021 0.024 0.004 -0.767
HMC 50.0 0.019 0.022 0.003 -1.059
SMC 2.1 1.416 0.068 0.022 61.285
SMC 3.0 0.504 0.036 0.004 112.294
SMC 4.0 0.305 0.032 0.003 79.628
SMC 10.0 0.174 0.024 0.004 40.914
SMC 50.0 0.074 0.022 0.003 16.049
Metro 2.1 0.252 0.068 0.022 8.376
Metro 3.0 0.092 0.036 0.004 13.368
Metro 4.0 0.065 0.032 0.003 9.814
Metro 10.0 0.049 0.024 0.004 6.948
Metro 50.0 0.042 0.022 0.003 6.048
DEMetro_Z 2.1 7.485 0.068 0.022 337.269
DEMetro_Z 3.0 2.537 0.036 0.004 600.693
DEMetro_Z 4.0 1.342 0.032 0.003 381.502
DEMetro_Z 10.0 1.024 0.024 0.004 273.200
DEMetro_Z 50.0 0.560 0.022 0.003 166.381
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.036 0.972 -0.010
HMC 3.0 1.254 0.225 2.210
HMC 4.0 1.698 0.106 3.741
HMC 10.0 5.709 6.83e-06 3.664
HMC 50.0 7.632 3.65e-09 2.518
SMC 2.1 72.958 3.75e-25 157.484
SMC 3.0 84.473 5.82e-26 813.581
SMC 4.0 50.061 1.21e-21 3668.885
SMC 10.0 70.560 1.85e-24 13601.849
SMC 50.0 28.284 5.41e-17 1189.387
Metro 2.1 1.671 0.106 0.803
Metro 3.0 3.691 0.000879 1.663
Metro 4.0 3.863 0.000947 4.763
Metro 10.0 6.953 1.01e-06 10.995
Metro 50.0 11.939 4.42e-12 6.619
DEMetro_Z 2.1 7.967 1.59e-07 19.898
DEMetro_Z 3.0 10.151 4.07e-09 85.173
DEMetro_Z 4.0 8.200 1.16e-07 219.591
DEMetro_Z 10.0 5.870 1.18e-05 873.468
DEMetro_Z 50.0 3.852 0.00107 301.042
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -71.636 1.39e-24 -16.018
HMC_vs_SMC 1 -85.221 5.18e-26 -19.056
HMC_vs_SMC 2 -50.305 1.11e-21 -11.249
HMC_vs_SMC 3 -70.594 1.83e-24 -15.785
HMC_vs_SMC 4 -28.249 5.54e-17 -6.317
Metro_vs_DEMetro_Z 0 -7.393 5.3e-07 -1.653
Metro_vs_DEMetro_Z 1 -9.988 5.36e-09 -2.233
Metro_vs_DEMetro_Z 2 -8.073 1.46e-07 -1.805
Metro_vs_DEMetro_Z 3 -5.799 1.38e-05 -1.297
Metro_vs_DEMetro_Z 4 -3.775 0.00128 -0.844
HMC_vs_Metro 0 -2.022 0.0575 -0.452
HMC_vs_Metro 1 0.314 0.757 0.070
HMC_vs_Metro 2 -0.430 0.672 -0.096
HMC_vs_Metro 3 -3.865 0.00104 -0.864
HMC_vs_Metro 4 -6.325 4.54e-06 -1.414
HMC_vs_DEMetro_Z 0 -7.771 2.57e-07 -1.738
HMC_vs_DEMetro_Z 1 -9.247 1.83e-08 -2.068
HMC_vs_DEMetro_Z 2 -7.868 2.14e-07 -1.759
HMC_vs_DEMetro_Z 3 -5.844 1.25e-05 -1.307
HMC_vs_DEMetro_Z 4 -3.817 0.00116 -0.853
Metro_vs_SMC 0 -66.472 5.73e-24 -14.864
Metro_vs_SMC 1 -84.473 6.12e-26 -18.889
Metro_vs_SMC 2 -50.044 1.22e-21 -11.190
Metro_vs_SMC 3 -70.463 1.9e-24 -15.756
Metro_vs_SMC 4 -28.108 6.08e-17 -6.285
DEMetro_Z_vs_SMC 0 -42.753 2.38e-20 -9.560
DEMetro_Z_vs_SMC 1 -51.889 6.18e-22 -11.603
DEMetro_Z_vs_SMC 2 -45.575 7.14e-21 -10.191
DEMetro_Z_vs_SMC 3 -59.218 5.09e-23 -13.242
DEMetro_Z_vs_SMC 4 -9.815 7.1e-09 -2.195
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 8.140 8.319 17.897 -0.010
HMC 3.0 1.729 0.639 0.493 2.210
HMC 4.0 0.341 0.164 0.047 3.741
HMC 10.0 0.069 0.048 0.006 3.664
HMC 50.0 0.045 0.033 0.005 2.518
SMC 2.1 2826.811 8.319 17.897 157.484
SMC 3.0 401.947 0.639 0.493 813.581
SMC 4.0 173.609 0.164 0.047 3668.885
SMC 10.0 77.583 0.048 0.006 13601.849
SMC 50.0 5.488 0.033 0.005 1189.387
Metro 2.1 22.698 8.319 17.897 0.803
Metro 3.0 1.459 0.639 0.493 1.663
Metro 4.0 0.390 0.164 0.047 4.763
Metro 10.0 0.111 0.048 0.006 10.995
Metro 50.0 0.064 0.033 0.005 6.619
DEMetro_Z 2.1 364.430 8.319 17.897 19.898
DEMetro_Z 3.0 42.651 0.639 0.493 85.173
DEMetro_Z 4.0 10.545 0.164 0.047 219.591
DEMetro_Z 10.0 5.027 0.048 0.006 873.468
DEMetro_Z 50.0 1.414 0.033 0.005 301.042
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.067 0.00626 7.576
HMC 3.0 1.758 0.0949 39.977
HMC 4.0 1.453 0.163 18.535
HMC 10.0 2.364 0.0237 0.876
HMC 50.0 -0.415 0.68 -0.123
SMC 2.1 138.172 5.14e-30 1453.877
SMC 3.0 155.814 5.45e-31 3199.474
SMC 4.0 85.738 4.6e-26 3381.863
SMC 10.0 119.179 8.86e-29 2700.172
SMC 50.0 40.060 7.97e-20 644.463
Metro 2.1 3.792 0.00123 31.380
Metro 3.0 9.046 2.41e-08 31.609
Metro 4.0 7.327 5.58e-07 20.479
Metro 10.0 12.948 9.39e-12 10.750
Metro 50.0 14.956 1.86e-14 8.062
DEMetro_Z 2.1 17.027 5.79e-13 479.261
DEMetro_Z 3.0 18.216 1.73e-13 913.623
DEMetro_Z 4.0 13.495 3.48e-11 643.475
DEMetro_Z 10.0 14.927 5.99e-12 520.171
DEMetro_Z 50.0 11.751 3.68e-10 289.597
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -16.370 1.17e-12 -3.660
Metro_vs_DEMetro_Z 1 -17.967 2.21e-13 -4.018
Metro_vs_DEMetro_Z 2 -13.116 5.69e-11 -2.933
Metro_vs_DEMetro_Z 3 -14.708 7.77e-12 -3.289
Metro_vs_DEMetro_Z 4 -11.402 6.11e-10 -2.550
DEMetro_Z_vs_SMC 0 -32.273 4.63e-18 -7.217
DEMetro_Z_vs_SMC 1 -40.677 6.06e-20 -9.096
DEMetro_Z_vs_SMC 2 -48.622 2.11e-21 -10.872
DEMetro_Z_vs_SMC 3 -60.286 3.63e-23 -13.480
DEMetro_Z_vs_SMC 4 -11.230 7.87e-10 -2.511
HMC_vs_DEMetro_Z 0 -16.670 8.48e-13 -3.728
HMC_vs_DEMetro_Z 1 -13.845 2.23e-11 -3.096
HMC_vs_DEMetro_Z 2 -11.798 3.45e-10 -2.638
HMC_vs_DEMetro_Z 3 -14.916 6.08e-12 -3.335
HMC_vs_DEMetro_Z 4 -11.744 3.73e-10 -2.626
HMC_vs_Metro 0 -2.749 0.0128 -0.615
HMC_vs_Metro 1 0.371 0.715 0.083
HMC_vs_Metro 2 -0.149 0.883 -0.033
HMC_vs_Metro 3 -10.795 1.51e-09 -2.414
HMC_vs_Metro 4 -16.802 7.36e-13 -3.757
HMC_vs_SMC 0 -129.413 1.87e-29 -28.938
HMC_vs_SMC 1 -115.441 1.64e-28 -25.813
HMC_vs_SMC 2 -86.616 3.81e-26 -19.368
HMC_vs_SMC 3 -119.065 9.12e-29 -26.624
HMC_vs_SMC 4 -40.047 8.13e-20 -8.955
Metro_vs_SMC 0 -90.560 1.64e-26 -20.250
Metro_vs_SMC 1 -147.318 1.6e-30 -32.941
Metro_vs_SMC 2 -85.111 5.31e-26 -19.031
Metro_vs_SMC 3 -118.838 9.45e-29 -26.573
Metro_vs_SMC 4 -39.441 1.08e-19 -8.819
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.328 0.116 0.028 7.576
HMC 3.0 0.249 0.064 0.005 39.977
HMC 4.0 0.101 0.049 0.003 18.535
HMC 10.0 0.035 0.033 0.002 0.876
HMC 50.0 0.029 0.029 0.002 -0.123
SMC 2.1 40.898 0.116 0.028 1453.877
SMC 3.0 14.882 0.064 0.005 3199.474
SMC 4.0 9.540 0.049 0.003 3381.863
SMC 10.0 6.208 0.033 0.002 2700.172
SMC 50.0 1.235 0.029 0.002 644.463
Metro 2.1 0.996 0.116 0.028 31.380
Metro 3.0 0.210 0.064 0.005 31.609
Metro 4.0 0.107 0.049 0.003 20.479
Metro 10.0 0.058 0.033 0.002 10.750
Metro 50.0 0.044 0.029 0.002 8.062
DEMetro_Z 2.1 13.560 0.116 0.028 479.261
DEMetro_Z 3.0 4.295 0.064 0.005 913.623
DEMetro_Z 4.0 1.855 0.049 0.003 643.475
DEMetro_Z 10.0 1.223 0.033 0.002 520.171
DEMetro_Z 50.0 0.571 0.029 0.002 289.597
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.678 0.0149 33.221
HMC 3.0 1.783 0.0906 27.790
HMC 4.0 1.442 0.166 15.817
HMC 10.0 1.271 0.212 0.469
HMC 50.0 -0.940 0.353 -0.289
SMC 2.1 152.655 7.06e-32 238.162
SMC 3.0 184.168 1.1e-34 201.979
SMC 4.0 136.691 2.36e-30 320.705
SMC 10.0 159.102 2.91e-32 245.006
SMC 50.0 87.330 9.7e-27 174.595
Metro 2.1 6.423 3.69e-06 80.392
Metro 3.0 7.808 2.22e-07 23.325
Metro 4.0 9.093 1.98e-08 19.601
Metro 10.0 12.661 7.17e-12 9.044
Metro 50.0 13.444 6.63e-14 6.489
DEMetro_Z 2.1 58.624 5.38e-23 320.677
DEMetro_Z 3.0 46.289 4.71e-21 251.217
DEMetro_Z 4.0 29.758 2.06e-17 333.828
DEMetro_Z 10.0 34.299 1.4e-18 248.917
DEMetro_Z 50.0 17.681 2.89e-13 164.681
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 14.079 1.67e-11 3.148
DEMetro_Z_vs_SMC 1 8.961 2.99e-08 2.004
DEMetro_Z_vs_SMC 2 1.158 0.261 0.259
DEMetro_Z_vs_SMC 3 0.542 0.594 0.121
DEMetro_Z_vs_SMC 4 -1.001 0.329 -0.224
HMC_vs_Metro 0 -2.562 0.0191 -0.573
HMC_vs_Metro 1 0.285 0.779 0.064
HMC_vs_Metro 2 -0.337 0.74 -0.075
HMC_vs_Metro 3 -10.799 1.51e-09 -2.415
HMC_vs_Metro 4 -15.267 4.04e-12 -3.414
Metro_vs_DEMetro_Z 0 -17.016 5.88e-13 -3.805
Metro_vs_DEMetro_Z 1 -34.933 1.05e-18 -7.811
Metro_vs_DEMetro_Z 2 -27.468 9.32e-17 -6.142
Metro_vs_DEMetro_Z 3 -32.308 4.54e-18 -7.224
Metro_vs_DEMetro_Z 4 -16.755 7.74e-13 -3.747
HMC_vs_SMC 0 -16.026 1.71e-12 -3.584
HMC_vs_SMC 1 -11.055 1.02e-09 -2.472
HMC_vs_SMC 2 -26.982 1.3e-16 -6.033
HMC_vs_SMC 3 -156.930 4.83e-31 -35.091
HMC_vs_SMC 4 -88.398 2.59e-26 -19.766
Metro_vs_SMC 0 -12.532 1.24e-10 -2.802
Metro_vs_SMC 1 -62.100 2.07e-23 -13.886
Metro_vs_SMC 2 -105.181 9.58e-28 -23.519
Metro_vs_SMC 3 -126.339 2.96e-29 -28.250
Metro_vs_SMC 4 -83.341 7.91e-26 -18.636
HMC_vs_DEMetro_Z 0 -20.482 2.06e-14 -4.580
HMC_vs_DEMetro_Z 1 -12.010 2.55e-10 -2.686
HMC_vs_DEMetro_Z 2 -19.704 4.18e-14 -4.406
HMC_vs_DEMetro_Z 3 -34.914 1.06e-18 -7.807
HMC_vs_DEMetro_Z 4 -17.691 2.93e-13 -3.956
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.071 0.015 0.002 33.221
HMC 3.0 0.069 0.015 0.002 27.790
HMC 4.0 0.034 0.015 0.001 15.817
HMC 10.0 0.015 0.014 0.002 0.469
HMC 50.0 0.013 0.014 0.002 -0.289
SMC 2.1 0.416 0.015 0.002 238.162
SMC 3.0 0.410 0.015 0.002 201.979
SMC 4.0 0.403 0.015 0.001 320.705
SMC 10.0 0.401 0.014 0.002 245.006
SMC 50.0 0.292 0.014 0.002 174.595
Metro 2.1 0.150 0.015 0.002 80.392
Metro 3.0 0.060 0.015 0.002 23.325
Metro 4.0 0.039 0.015 0.001 19.601
Metro 10.0 0.028 0.014 0.002 9.044
Metro 50.0 0.024 0.014 0.002 6.489
DEMetro_Z 2.1 0.554 0.015 0.002 320.677
DEMetro_Z 3.0 0.506 0.015 0.002 251.217
DEMetro_Z 4.0 0.419 0.015 0.001 333.828
DEMetro_Z 10.0 0.407 0.014 0.002 248.917
DEMetro_Z 50.0 0.276 0.014 0.002 164.681
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Varying_Tails_with_high_Correlation (MvStudentT, nu, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.033 0.974 0.010
HMC 3.0 1.095 0.281 0.398
HMC 4.0 3.032 0.0045 1.104
HMC 10.0 0.337 0.738 0.109
HMC 50.0 1.377 0.178 0.607
SMC 2.1 2.055 0.0505 1.223
SMC 3.0 -0.356 0.724 -0.093
SMC 4.0 -0.015 0.988 -0.005
SMC 10.0 -0.867 0.392 -0.233
SMC 50.0 -1.029 0.311 -0.269
Metro 2.1 2.797 0.011 3.401
Metro 3.0 3.668 0.00151 4.783
Metro 4.0 6.087 5.5e-06 7.209
Metro 10.0 5.903 7.1e-06 5.640
Metro 50.0 4.016 0.00065 4.595
DEMetro_Z 2.1 2.683 0.0136 2.292
DEMetro_Z 3.0 3.146 0.0039 1.566
DEMetro_Z 4.0 3.696 0.00122 2.828
DEMetro_Z 10.0 3.450 0.00153 1.359
DEMetro_Z 50.0 3.305 0.00267 1.717
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.002 0.00732 -0.671
HMC_vs_DEMetro_Z 1 -2.172 0.0428 -0.486
HMC_vs_DEMetro_Z 2 -2.044 0.0551 -0.457
HMC_vs_DEMetro_Z 3 -3.431 0.0028 -0.767
HMC_vs_DEMetro_Z 4 -1.711 0.103 -0.383
Metro_vs_SMC 0 1.653 0.115 0.370
Metro_vs_SMC 1 3.920 0.00092 0.877
Metro_vs_SMC 2 6.199 5.9e-06 1.386
Metro_vs_SMC 3 6.019 8.62e-06 1.346
Metro_vs_SMC 4 4.152 0.000542 0.928
Metro_vs_DEMetro_Z 0 0.698 0.494 0.156
Metro_vs_DEMetro_Z 1 2.315 0.0319 0.518
Metro_vs_DEMetro_Z 2 2.724 0.0135 0.609
Metro_vs_DEMetro_Z 3 4.399 0.000308 0.984
Metro_vs_DEMetro_Z 4 2.301 0.0329 0.514
HMC_vs_Metro 0 -2.841 0.0104 -0.635
HMC_vs_Metro 1 -3.596 0.00193 -0.804
HMC_vs_Metro 2 -5.117 6.12e-05 -1.144
HMC_vs_Metro 3 -5.516 2.54e-05 -1.234
HMC_vs_Metro 4 -3.475 0.00253 -0.777
HMC_vs_SMC 0 -2.305 0.0326 -0.516
HMC_vs_SMC 1 1.976 0.0629 0.442
HMC_vs_SMC 2 3.868 0.00104 0.865
HMC_vs_SMC 3 1.385 0.182 0.310
HMC_vs_SMC 4 2.300 0.0329 0.514
DEMetro_Z_vs_SMC 0 2.064 0.053 0.461
DEMetro_Z_vs_SMC 1 3.435 0.00278 0.768
DEMetro_Z_vs_SMC 2 3.579 0.002 0.800
DEMetro_Z_vs_SMC 3 4.987 8.18e-05 1.115
DEMetro_Z_vs_SMC 4 3.992 0.00078 0.893
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.067 0.067 0.049 0.010
HMC 3.0 0.049 0.038 0.028 0.398
HMC 4.0 0.042 0.024 0.017 1.104
HMC 10.0 0.026 0.024 0.019 0.109
HMC 50.0 0.033 0.023 0.016 0.607
SMC 2.1 0.127 0.067 0.049 1.223
SMC 3.0 0.035 0.038 0.028 -0.093
SMC 4.0 0.024 0.024 0.017 -0.005
SMC 10.0 0.020 0.024 0.019 -0.233
SMC 50.0 0.019 0.023 0.016 -0.269
Metro 2.1 0.233 0.067 0.049 3.401
Metro 3.0 0.172 0.038 0.028 4.783
Metro 4.0 0.144 0.024 0.017 7.209
Metro 10.0 0.129 0.024 0.019 5.640
Metro 50.0 0.097 0.023 0.016 4.595
DEMetro_Z 2.1 0.179 0.067 0.049 2.292
DEMetro_Z 3.0 0.082 0.038 0.028 1.566
DEMetro_Z 4.0 0.071 0.024 0.017 2.828
DEMetro_Z 10.0 0.049 0.024 0.019 1.359
DEMetro_Z 50.0 0.051 0.023 0.016 1.717
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.954 0.35 -0.226
HMC 3.0 1.107 0.276 0.423
HMC 4.0 0.945 0.351 0.306
HMC 10.0 2.019 0.0557 1.599
HMC 50.0 1.566 0.127 0.658
SMC 2.1 2.708 0.0107 0.719
SMC 3.0 1.114 0.273 0.418
SMC 4.0 0.721 0.476 0.198
SMC 10.0 0.487 0.629 0.164
SMC 50.0 -0.142 0.888 -0.044
Metro 2.1 -0.369 0.715 -0.093
Metro 3.0 2.640 0.0139 1.481
Metro 4.0 2.166 0.0392 1.119
Metro 10.0 5.242 3.31e-05 5.039
Metro 50.0 4.043 0.000436 2.373
DEMetro_Z 2.1 -0.657 0.517 -0.157
DEMetro_Z 3.0 2.791 0.00901 1.254
DEMetro_Z 4.0 1.749 0.0947 1.646
DEMetro_Z 10.0 2.526 0.0174 1.234
DEMetro_Z 50.0 0.676 0.504 0.276
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -5.665 1.84e-05 -1.267
HMC_vs_SMC 1 0.013 0.99 0.003
HMC_vs_SMC 2 0.376 0.711 0.084
HMC_vs_SMC 3 1.714 0.103 0.383
HMC_vs_SMC 4 1.740 0.098 0.389
Metro_vs_DEMetro_Z 0 0.654 0.521 0.146
Metro_vs_DEMetro_Z 1 0.548 0.59 0.123
Metro_vs_DEMetro_Z 2 -0.519 0.61 -0.116
Metro_vs_DEMetro_Z 3 4.612 0.00019 1.031
Metro_vs_DEMetro_Z 4 3.359 0.0033 0.751
HMC_vs_Metro 0 -1.336 0.197 -0.299
HMC_vs_Metro 1 -1.827 0.0834 -0.409
HMC_vs_Metro 2 -1.599 0.126 -0.357
HMC_vs_Metro 3 -2.914 0.00889 -0.652
HMC_vs_Metro 4 -2.924 0.00872 -0.654
HMC_vs_DEMetro_Z 0 -2.320 0.0316 -0.519
HMC_vs_DEMetro_Z 1 -2.096 0.0497 -0.469
HMC_vs_DEMetro_Z 2 -1.317 0.204 -0.294
HMC_vs_DEMetro_Z 3 0.382 0.707 0.085
HMC_vs_DEMetro_Z 4 0.797 0.435 0.178
Metro_vs_SMC 0 -5.325 3.86e-05 -1.191
Metro_vs_SMC 1 2.079 0.0514 0.465
Metro_vs_SMC 2 1.779 0.0913 0.398
Metro_vs_SMC 3 4.839 0.000114 1.082
Metro_vs_SMC 4 4.222 0.000461 0.944
DEMetro_Z_vs_SMC 0 -5.009 7.78e-05 -1.120
DEMetro_Z_vs_SMC 1 1.909 0.0715 0.427
DEMetro_Z_vs_SMC 2 1.600 0.126 0.358
DEMetro_Z_vs_SMC 3 2.436 0.0249 0.545
DEMetro_Z_vs_SMC 4 0.720 0.48 0.161
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 5.023 8.853 16.927 -0.226
HMC 3.0 0.602 0.454 0.349 0.423
HMC 4.0 0.211 0.160 0.167 0.306
HMC 10.0 0.086 0.044 0.027 1.599
HMC 50.0 0.050 0.036 0.020 0.658
SMC 2.1 21.024 8.853 16.927 0.719
SMC 3.0 0.600 0.454 0.349 0.418
SMC 4.0 0.193 0.160 0.167 0.198
SMC 10.0 0.048 0.044 0.027 0.164
SMC 50.0 0.036 0.036 0.020 -0.044
Metro 2.1 7.273 8.853 16.927 -0.093
Metro 3.0 0.971 0.454 0.349 1.481
Metro 4.0 0.347 0.160 0.167 1.119
Metro 10.0 0.179 0.044 0.027 5.039
Metro 50.0 0.084 0.036 0.020 2.373
DEMetro_Z 2.1 6.200 8.853 16.927 -0.157
DEMetro_Z 3.0 0.892 0.454 0.349 1.254
DEMetro_Z 4.0 0.435 0.160 0.167 1.646
DEMetro_Z 10.0 0.077 0.044 0.027 1.234
DEMetro_Z 50.0 0.042 0.036 0.020 0.276
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.909 0.000377 1.162
HMC 3.0 4.236 0.000148 1.507
HMC 4.0 5.181 1.6e-05 2.510
HMC 10.0 2.018 0.0527 0.936
HMC 50.0 2.280 0.0303 1.109
SMC 2.1 11.109 7.68e-10 26.085
SMC 3.0 2.409 0.022 1.024
SMC 4.0 0.676 0.503 0.239
SMC 10.0 -0.931 0.358 -0.261
SMC 50.0 -0.578 0.568 -0.148
Metro 2.1 3.488 0.00237 6.270
Metro 3.0 6.421 2.79e-06 8.294
Metro 4.0 8.159 8.97e-08 12.104
Metro 10.0 7.290 4.21e-07 8.636
Metro 50.0 4.489 0.00023 7.080
DEMetro_Z 2.1 5.150 3.56e-05 4.112
DEMetro_Z 3.0 8.919 9.19e-10 4.306
DEMetro_Z 4.0 5.742 1.18e-05 6.767
DEMetro_Z 10.0 5.708 2.89e-06 2.513
DEMetro_Z 50.0 4.368 0.000193 2.637
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.097 0.287 0.245
Metro_vs_DEMetro_Z 1 3.132 0.00549 0.700
Metro_vs_DEMetro_Z 2 2.529 0.0204 0.566
Metro_vs_DEMetro_Z 3 5.093 6.47e-05 1.139
Metro_vs_DEMetro_Z 4 2.558 0.0192 0.572
DEMetro_Z_vs_SMC 0 -9.097 2.36e-08 -2.034
DEMetro_Z_vs_SMC 1 6.089 7.44e-06 1.362
DEMetro_Z_vs_SMC 2 5.689 1.75e-05 1.272
DEMetro_Z_vs_SMC 3 6.987 1.18e-06 1.562
DEMetro_Z_vs_SMC 4 5.077 6.7e-05 1.135
HMC_vs_DEMetro_Z 0 -3.609 0.00187 -0.807
HMC_vs_DEMetro_Z 1 -5.375 3.47e-05 -1.202
HMC_vs_DEMetro_Z 2 -3.334 0.00349 -0.745
HMC_vs_DEMetro_Z 3 -3.080 0.00616 -0.689
HMC_vs_DEMetro_Z 4 -1.905 0.072 -0.426
HMC_vs_Metro 0 -2.801 0.0114 -0.626
HMC_vs_Metro 1 -5.572 2.25e-05 -1.246
HMC_vs_Metro 2 -6.314 4.64e-06 -1.412
HMC_vs_Metro 3 -5.901 1.11e-05 -1.320
HMC_vs_Metro 4 -3.788 0.00124 -0.847
HMC_vs_SMC 0 -10.780 1.55e-09 -2.410
HMC_vs_SMC 1 1.148 0.265 0.257
HMC_vs_SMC 2 4.675 0.000165 1.045
HMC_vs_SMC 3 2.877 0.00966 0.643
HMC_vs_SMC 4 2.886 0.00947 0.645
Metro_vs_SMC 0 -8.769 4.18e-08 -1.961
Metro_vs_SMC 1 5.458 2.89e-05 1.220
Metro_vs_SMC 2 7.685 3.03e-07 1.718
Metro_vs_SMC 3 7.366 5.59e-07 1.647
Metro_vs_SMC 4 4.536 0.000226 1.014
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.165 0.119 0.040 1.162
HMC 3.0 0.092 0.063 0.019 1.507
HMC 4.0 0.068 0.045 0.009 2.510
HMC 10.0 0.046 0.035 0.012 0.936
HMC 50.0 0.042 0.031 0.010 1.109
SMC 2.1 1.154 0.119 0.040 26.085
SMC 3.0 0.083 0.063 0.019 1.024
SMC 4.0 0.047 0.045 0.009 0.239
SMC 10.0 0.032 0.035 0.012 -0.261
SMC 50.0 0.029 0.031 0.010 -0.148
Metro 2.1 0.368 0.119 0.040 6.270
Metro 3.0 0.223 0.063 0.019 8.294
Metro 4.0 0.157 0.045 0.009 12.104
Metro 10.0 0.135 0.035 0.012 8.636
Metro 50.0 0.102 0.031 0.010 7.080
DEMetro_Z 2.1 0.282 0.119 0.040 4.112
DEMetro_Z 3.0 0.146 0.063 0.019 4.306
DEMetro_Z 4.0 0.108 0.045 0.009 6.767
DEMetro_Z 10.0 0.064 0.035 0.012 2.513
DEMetro_Z 50.0 0.057 0.031 0.010 2.637
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.718 5.64e-05 2.261
HMC 3.0 3.191 0.00302 1.221
HMC 4.0 3.394 0.00198 1.569
HMC 10.0 3.017 0.00548 1.569
HMC 50.0 1.721 0.0948 0.717
SMC 2.1 16.296 9.2e-13 37.830
SMC 3.0 2.953 0.00623 1.432
SMC 4.0 -0.165 0.87 -0.059
SMC 10.0 -0.348 0.73 -0.130
SMC 50.0 -0.037 0.971 -0.010
Metro 2.1 6.158 5.08e-06 8.425
Metro 3.0 8.321 4.58e-08 8.591
Metro 4.0 8.718 1.6e-08 7.690
Metro 10.0 7.961 1.09e-07 9.444
Metro 50.0 4.424 0.000257 5.705
DEMetro_Z 2.1 5.370 2.71e-05 6.101
DEMetro_Z 3.0 7.467 8.43e-08 4.529
DEMetro_Z 4.0 5.083 4.02e-05 3.878
DEMetro_Z 10.0 5.148 2.48e-05 3.037
DEMetro_Z 50.0 3.532 0.00159 2.030
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -14.684 8e-12 -3.283
DEMetro_Z_vs_SMC 1 4.550 0.000219 1.017
DEMetro_Z_vs_SMC 2 5.140 5.82e-05 1.149
DEMetro_Z_vs_SMC 3 5.452 2.93e-05 1.219
DEMetro_Z_vs_SMC 4 4.208 0.000477 0.941
HMC_vs_Metro 0 -4.291 0.000395 -0.959
HMC_vs_Metro 1 -7.680 3.06e-07 -1.717
HMC_vs_Metro 2 -6.807 1.69e-06 -1.522
HMC_vs_Metro 3 -6.151 6.53e-06 -1.375
HMC_vs_Metro 4 -3.830 0.00113 -0.856
Metro_vs_DEMetro_Z 0 1.380 0.184 0.309
Metro_vs_DEMetro_Z 1 3.747 0.00137 0.838
Metro_vs_DEMetro_Z 2 3.201 0.0047 0.716
Metro_vs_DEMetro_Z 3 4.533 0.000228 1.014
Metro_vs_DEMetro_Z 4 2.533 0.0203 0.566
HMC_vs_SMC 0 -16.092 1.59e-12 -3.598
HMC_vs_SMC 1 -0.417 0.682 -0.093
HMC_vs_SMC 2 3.415 0.0029 0.764
HMC_vs_SMC 3 3.072 0.00628 0.687
HMC_vs_SMC 4 2.046 0.0549 0.457
Metro_vs_SMC 0 -12.754 9.2e-11 -2.852
Metro_vs_SMC 1 5.906 1.1e-05 1.321
Metro_vs_SMC 2 8.961 2.99e-08 2.004
Metro_vs_SMC 3 7.501 4.3e-07 1.677
Metro_vs_SMC 4 4.440 0.000281 0.993
HMC_vs_DEMetro_Z 0 -3.301 0.00376 -0.738
HMC_vs_DEMetro_Z 1 -4.515 0.000237 -1.010
HMC_vs_DEMetro_Z 2 -3.529 0.00224 -0.789
HMC_vs_DEMetro_Z 3 -2.160 0.0437 -0.483
HMC_vs_DEMetro_Z 4 -1.867 0.0774 -0.417
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.026 0.014 0.005 2.261
HMC 3.0 0.021 0.015 0.005 1.221
HMC 4.0 0.022 0.014 0.005 1.569
HMC 10.0 0.022 0.015 0.005 1.569
HMC 50.0 0.020 0.015 0.006 0.717
SMC 2.1 0.209 0.014 0.005 37.830
SMC 3.0 0.022 0.015 0.005 1.432
SMC 4.0 0.014 0.014 0.005 -0.059
SMC 10.0 0.014 0.015 0.005 -0.130
SMC 50.0 0.015 0.015 0.006 -0.010
Metro 2.1 0.058 0.014 0.005 8.425
Metro 3.0 0.059 0.015 0.005 8.591
Metro 4.0 0.050 0.014 0.005 7.690
Metro 10.0 0.060 0.015 0.005 9.444
Metro 50.0 0.049 0.015 0.006 5.705
DEMetro_Z 2.1 0.046 0.014 0.005 6.101
DEMetro_Z 3.0 0.038 0.015 0.005 4.529
DEMetro_Z 4.0 0.032 0.014 0.005 3.878
DEMetro_Z 10.0 0.029 0.015 0.005 3.037
DEMetro_Z 50.0 0.027 0.015 0.006 2.030
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.158 0.255 0.433
HMC 3.0 1.217 0.232 0.468
HMC 4.0 2.342 0.0269 1.242
HMC 10.0 1.049 0.301 0.326
HMC 50.0 1.772 0.0857 0.725
SMC 2.1 3.150 0.00369 1.441
SMC 3.0 -0.334 0.741 -0.088
SMC 4.0 0.325 0.747 0.098
SMC 10.0 -0.675 0.504 -0.190
SMC 50.0 -1.632 0.113 -0.427
Metro 2.1 1.892 0.0737 7.513
Metro 3.0 2.996 0.00731 6.672
Metro 4.0 5.612 1.59e-05 6.633
Metro 10.0 4.170 0.000448 4.648
Metro 50.0 3.864 0.000885 3.686
DEMetro_Z 2.1 1.121 0.273 0.624
DEMetro_Z 3.0 2.324 0.0284 1.335
DEMetro_Z 4.0 3.732 0.000939 2.090
DEMetro_Z 10.0 2.412 0.0214 0.943
DEMetro_Z 50.0 2.428 0.0213 1.098
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.340 0.737 -0.076
HMC_vs_DEMetro_Z 1 -1.321 0.202 -0.295
HMC_vs_DEMetro_Z 2 -1.333 0.198 -0.298
HMC_vs_DEMetro_Z 3 -1.600 0.126 -0.358
HMC_vs_DEMetro_Z 4 -0.726 0.477 -0.162
Metro_vs_SMC 0 1.477 0.156 0.330
Metro_vs_SMC 1 3.063 0.0064 0.685
Metro_vs_SMC 2 5.878 1.16e-05 1.314
Metro_vs_SMC 3 4.445 0.000278 0.994
Metro_vs_SMC 4 4.313 0.000375 0.964
Metro_vs_DEMetro_Z 0 1.698 0.106 0.380
Metro_vs_DEMetro_Z 1 2.401 0.0268 0.537
Metro_vs_DEMetro_Z 2 4.269 0.000415 0.955
Metro_vs_DEMetro_Z 3 3.389 0.00308 0.758
Metro_vs_DEMetro_Z 4 2.698 0.0142 0.603
HMC_vs_Metro 0 -1.776 0.0918 -0.397
HMC_vs_Metro 1 -2.758 0.0125 -0.617
HMC_vs_Metro 2 -3.981 0.000799 -0.890
HMC_vs_Metro 3 -3.846 0.00109 -0.860
HMC_vs_Metro 4 -2.795 0.0115 -0.625
HMC_vs_SMC 0 -2.567 0.0189 -0.574
HMC_vs_SMC 1 1.787 0.09 0.399
HMC_vs_SMC 2 2.114 0.048 0.473
HMC_vs_SMC 3 1.826 0.0836 0.408
HMC_vs_SMC 4 3.127 0.00555 0.699
DEMetro_Z_vs_SMC 0 -1.539 0.14 -0.344
DEMetro_Z_vs_SMC 1 2.602 0.0175 0.582
DEMetro_Z_vs_SMC 2 4.082 0.000635 0.913
DEMetro_Z_vs_SMC 3 2.983 0.00764 0.667
DEMetro_Z_vs_SMC 4 4.212 0.000473 0.942
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.088 0.067 0.049 0.433
HMC 3.0 0.051 0.038 0.028 0.468
HMC 4.0 0.045 0.024 0.017 1.242
HMC 10.0 0.030 0.024 0.019 0.326
HMC 50.0 0.035 0.023 0.016 0.725
SMC 2.1 0.137 0.067 0.049 1.441
SMC 3.0 0.036 0.038 0.028 -0.088
SMC 4.0 0.026 0.024 0.017 0.098
SMC 10.0 0.021 0.024 0.019 -0.190
SMC 50.0 0.016 0.023 0.016 -0.427
Metro 2.1 0.433 0.067 0.049 7.513
Metro 3.0 0.225 0.038 0.028 6.672
Metro 4.0 0.135 0.024 0.017 6.633
Metro 10.0 0.110 0.024 0.019 4.648
Metro 50.0 0.083 0.023 0.016 3.686
DEMetro_Z 2.1 0.097 0.067 0.049 0.624
DEMetro_Z 3.0 0.075 0.038 0.028 1.335
DEMetro_Z 4.0 0.059 0.024 0.017 2.090
DEMetro_Z 10.0 0.042 0.024 0.019 0.943
DEMetro_Z 50.0 0.041 0.023 0.016 1.098
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.891 0.382 -0.211
HMC 3.0 1.537 0.134 0.644
HMC 4.0 1.995 0.0551 0.895
HMC 10.0 2.009 0.0543 1.006
HMC 50.0 0.208 0.836 0.071
SMC 2.1 0.216 0.831 0.053
SMC 3.0 0.866 0.393 0.351
SMC 4.0 0.893 0.378 0.239
SMC 10.0 -1.370 0.179 -0.391
SMC 50.0 -1.135 0.264 -0.322
Metro 2.1 0.686 0.5 0.534
Metro 3.0 1.541 0.139 3.671
Metro 4.0 3.367 0.00181 1.201
Metro 10.0 5.012 4.71e-05 3.752
Metro 50.0 4.238 0.000298 2.877
DEMetro_Z 2.1 -0.667 0.511 -0.159
DEMetro_Z 3.0 2.574 0.0172 1.978
DEMetro_Z 4.0 3.106 0.00358 1.003
DEMetro_Z 10.0 1.777 0.0849 0.732
DEMetro_Z 50.0 2.055 0.0493 1.011
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -2.237 0.0375 -0.500
HMC_vs_SMC 1 1.077 0.295 0.241
HMC_vs_SMC 2 1.575 0.132 0.352
HMC_vs_SMC 3 3.201 0.00471 0.716
HMC_vs_SMC 4 1.137 0.27 0.254
Metro_vs_DEMetro_Z 0 0.914 0.372 0.204
Metro_vs_DEMetro_Z 1 0.689 0.499 0.154
Metro_vs_DEMetro_Z 2 0.600 0.555 0.134
Metro_vs_DEMetro_Z 3 5.467 2.83e-05 1.222
Metro_vs_DEMetro_Z 4 2.219 0.0388 0.496
HMC_vs_Metro 0 -0.985 0.337 -0.220
HMC_vs_Metro 1 -1.273 0.218 -0.285
HMC_vs_Metro 2 -0.671 0.51 -0.150
HMC_vs_Metro 3 -3.408 0.00295 -0.762
HMC_vs_Metro 4 -4.644 0.000177 -1.038
HMC_vs_DEMetro_Z 0 -0.891 0.384 -0.199
HMC_vs_DEMetro_Z 1 -1.726 0.101 -0.386
HMC_vs_DEMetro_Z 2 -0.232 0.819 -0.052
HMC_vs_DEMetro_Z 3 0.524 0.607 0.117
HMC_vs_DEMetro_Z 4 -1.764 0.0937 -0.395
Metro_vs_SMC 0 0.618 0.544 0.138
Metro_vs_SMC 1 1.393 0.18 0.312
Metro_vs_SMC 2 3.618 0.00183 0.809
Metro_vs_SMC 3 5.622 2.02e-05 1.257
Metro_vs_SMC 4 4.554 0.000217 1.018
DEMetro_Z_vs_SMC 0 -2.143 0.0453 -0.479
DEMetro_Z_vs_SMC 1 2.496 0.0219 0.558
DEMetro_Z_vs_SMC 2 3.597 0.00192 0.804
DEMetro_Z_vs_SMC 3 3.054 0.00652 0.683
DEMetro_Z_vs_SMC 4 2.955 0.00813 0.661
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 5.274 8.853 16.927 -0.211
HMC 3.0 0.679 0.454 0.349 0.644
HMC 4.0 0.309 0.160 0.167 0.895
HMC 10.0 0.071 0.044 0.027 1.006
HMC 50.0 0.038 0.036 0.020 0.071
SMC 2.1 9.743 8.853 16.927 0.053
SMC 3.0 0.577 0.454 0.349 0.351
SMC 4.0 0.200 0.160 0.167 0.239
SMC 10.0 0.033 0.044 0.027 -0.391
SMC 50.0 0.030 0.036 0.020 -0.322
Metro 2.1 17.888 8.853 16.927 0.534
Metro 3.0 1.737 0.454 0.349 3.671
Metro 4.0 0.360 0.160 0.167 1.201
Metro 10.0 0.144 0.044 0.027 3.752
Metro 50.0 0.094 0.036 0.020 2.877
DEMetro_Z 2.1 6.157 8.853 16.927 -0.159
DEMetro_Z 3.0 1.145 0.454 0.349 1.978
DEMetro_Z 4.0 0.327 0.160 0.167 1.003
DEMetro_Z 10.0 0.063 0.044 0.027 0.732
DEMetro_Z 50.0 0.057 0.036 0.020 1.011
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.484 0.0187 1.096
HMC 3.0 3.916 0.00051 1.893
HMC 4.0 4.783 8.42e-05 3.655
HMC 10.0 2.107 0.0418 0.705
HMC 50.0 2.097 0.0447 0.979
SMC 2.1 6.573 2.4e-06 13.084
SMC 3.0 1.049 0.301 0.340
SMC 4.0 1.869 0.0693 0.588
SMC 10.0 -1.486 0.147 -0.400
SMC 50.0 -2.006 0.0545 -0.503
Metro 2.1 2.364 0.0288 9.799
Metro 3.0 3.701 0.00149 9.959
Metro 4.0 7.151 6.86e-07 11.795
Metro 10.0 5.670 1.49e-05 7.654
Metro 50.0 5.541 1.76e-05 5.870
DEMetro_Z 2.1 5.835 2.79e-06 2.882
DEMetro_Z 3.0 4.610 0.000143 4.109
DEMetro_Z 4.0 8.558 1e-08 5.672
DEMetro_Z 10.0 5.315 6.13e-06 1.991
DEMetro_Z 50.0 4.879 3.25e-05 2.208
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.614 0.123 0.361
Metro_vs_DEMetro_Z 1 2.141 0.0454 0.479
Metro_vs_DEMetro_Z 2 3.938 0.000882 0.881
Metro_vs_DEMetro_Z 3 4.364 0.000334 0.976
Metro_vs_DEMetro_Z 4 3.324 0.00356 0.743
DEMetro_Z_vs_SMC 0 -5.355 3.62e-05 -1.197
DEMetro_Z_vs_SMC 1 4.414 0.000298 0.987
DEMetro_Z_vs_SMC 2 7.961 1.8e-07 1.780
DEMetro_Z_vs_SMC 3 7.981 1.74e-07 1.785
DEMetro_Z_vs_SMC 4 7.442 4.82e-07 1.664
HMC_vs_DEMetro_Z 0 -3.183 0.0049 -0.712
HMC_vs_DEMetro_Z 1 -2.330 0.031 -0.521
HMC_vs_DEMetro_Z 2 -2.572 0.0187 -0.575
HMC_vs_DEMetro_Z 3 -3.390 0.00307 -0.758
HMC_vs_DEMetro_Z 4 -2.116 0.0477 -0.473
HMC_vs_Metro 0 -2.057 0.0537 -0.460
HMC_vs_Metro 1 -2.932 0.00855 -0.656
HMC_vs_Metro 2 -4.650 0.000174 -1.040
HMC_vs_Metro 3 -4.944 9.01e-05 -1.106
HMC_vs_Metro 4 -4.162 0.00053 -0.931
HMC_vs_SMC 0 -5.775 1.45e-05 -1.291
HMC_vs_SMC 1 3.554 0.00212 0.795
HMC_vs_SMC 2 3.930 0.000899 0.879
HMC_vs_SMC 3 3.879 0.00101 0.867
HMC_vs_SMC 4 3.636 0.00176 0.813
Metro_vs_SMC 0 -0.628 0.538 -0.140
Metro_vs_SMC 1 3.537 0.0022 0.791
Metro_vs_SMC 2 6.853 1.54e-06 1.532
Metro_vs_SMC 3 6.187 6.05e-06 1.383
Metro_vs_SMC 4 6.047 8.13e-06 1.352
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.162 0.119 0.040 1.096
HMC 3.0 0.100 0.063 0.019 1.893
HMC 4.0 0.079 0.045 0.009 3.655
HMC 10.0 0.043 0.035 0.012 0.705
HMC 50.0 0.041 0.031 0.010 0.979
SMC 2.1 0.638 0.119 0.040 13.084
SMC 3.0 0.070 0.063 0.019 0.340
SMC 4.0 0.050 0.045 0.009 0.588
SMC 10.0 0.030 0.035 0.012 -0.400
SMC 50.0 0.026 0.031 0.010 -0.503
Metro 2.1 0.508 0.119 0.040 9.799
Metro 3.0 0.255 0.063 0.019 9.959
Metro 4.0 0.154 0.045 0.009 11.795
Metro 10.0 0.124 0.035 0.012 7.654
Metro 50.0 0.090 0.031 0.010 5.870
DEMetro_Z 2.1 0.233 0.119 0.040 2.882
DEMetro_Z 3.0 0.142 0.063 0.019 4.109
DEMetro_Z 4.0 0.097 0.045 0.009 5.672
DEMetro_Z 10.0 0.058 0.035 0.012 1.991
DEMetro_Z 50.0 0.053 0.031 0.010 2.208
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.559 0.00146 1.987
HMC 3.0 3.109 0.00436 1.611
HMC 4.0 4.719 6.64e-05 2.520
HMC 10.0 2.127 0.0406 0.810
HMC 50.0 1.743 0.0913 0.757
SMC 2.1 8.413 7.24e-08 25.550
SMC 3.0 1.333 0.191 0.481
SMC 4.0 0.415 0.68 0.125
SMC 10.0 -1.700 0.0974 -0.514
SMC 50.0 -1.696 0.102 -0.411
Metro 2.1 5.652 1.64e-05 9.103
Metro 3.0 7.974 1.12e-07 9.907
Metro 4.0 7.954 7.64e-08 7.137
Metro 10.0 6.182 4.97e-06 9.052
Metro 50.0 5.292 3.07e-05 5.448
DEMetro_Z 2.1 5.337 1.95e-05 3.724
DEMetro_Z 3.0 5.119 2.87e-05 3.165
DEMetro_Z 4.0 6.948 2.54e-07 4.038
DEMetro_Z 10.0 5.081 2.25e-05 2.550
DEMetro_Z 50.0 5.060 1.71e-05 2.149
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -7.194 7.82e-07 -1.609
DEMetro_Z_vs_SMC 1 4.086 0.00063 0.914
DEMetro_Z_vs_SMC 2 6.548 2.86e-06 1.464
DEMetro_Z_vs_SMC 3 7.174 8.12e-07 1.604
DEMetro_Z_vs_SMC 4 7.156 8.43e-07 1.600
HMC_vs_Metro 0 -4.273 0.000411 -0.955
HMC_vs_Metro 1 -6.120 6.97e-06 -1.368
HMC_vs_Metro 2 -4.248 0.000435 -0.950
HMC_vs_Metro 3 -5.425 3.1e-05 -1.213
HMC_vs_Metro 4 -4.145 0.000551 -0.927
Metro_vs_DEMetro_Z 0 2.998 0.0074 0.670
Metro_vs_DEMetro_Z 1 4.816 0.00012 1.077
Metro_vs_DEMetro_Z 2 2.879 0.00962 0.644
Metro_vs_DEMetro_Z 3 4.697 0.000157 1.050
Metro_vs_DEMetro_Z 4 2.894 0.0093 0.647
HMC_vs_SMC 0 -7.634 3.34e-07 -1.707
HMC_vs_SMC 1 2.379 0.028 0.532
HMC_vs_SMC 2 4.689 0.00016 1.049
HMC_vs_SMC 3 3.692 0.00155 0.825
HMC_vs_SMC 4 3.400 0.003 0.760
Metro_vs_SMC 0 -4.943 9.02e-05 -1.105
Metro_vs_SMC 1 7.817 2.36e-07 1.748
Metro_vs_SMC 2 8.274 1.01e-07 1.850
Metro_vs_SMC 3 6.878 1.46e-06 1.538
Metro_vs_SMC 4 5.705 1.69e-05 1.276
HMC_vs_DEMetro_Z 0 -2.118 0.0476 -0.474
HMC_vs_DEMetro_Z 1 -2.507 0.0214 -0.561
HMC_vs_DEMetro_Z 2 -2.191 0.0412 -0.490
HMC_vs_DEMetro_Z 3 -3.149 0.00528 -0.704
HMC_vs_DEMetro_Z 4 -2.724 0.0135 -0.609
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.025 0.014 0.005 1.987
HMC 3.0 0.023 0.015 0.005 1.611
HMC 4.0 0.026 0.014 0.005 2.520
HMC 10.0 0.019 0.015 0.005 0.810
HMC 50.0 0.020 0.015 0.006 0.757
SMC 2.1 0.146 0.014 0.005 25.550
SMC 3.0 0.017 0.015 0.005 0.481
SMC 4.0 0.015 0.014 0.005 0.125
SMC 10.0 0.012 0.015 0.005 -0.514
SMC 50.0 0.013 0.015 0.006 -0.411
Metro 2.1 0.061 0.014 0.005 9.103
Metro 3.0 0.066 0.015 0.005 9.907
Metro 4.0 0.047 0.014 0.005 7.137
Metro 10.0 0.058 0.015 0.005 9.052
Metro 50.0 0.048 0.015 0.006 5.448
DEMetro_Z 2.1 0.033 0.014 0.005 3.724
DEMetro_Z 3.0 0.031 0.015 0.005 3.165
DEMetro_Z 4.0 0.033 0.014 0.005 4.038
DEMetro_Z 10.0 0.027 0.015 0.005 2.550
DEMetro_Z 50.0 0.028 0.015 0.006 2.149
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Vary_Tails_with_high_Multimodality (Mixture, nu, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.985 7.95e-06 9.853
HMC 3.0 6.143 5.95e-06 12.306
HMC 4.0 6.484 3.01e-06 15.987
HMC 10.0 4.286 0.000395 20.197
HMC 50.0 5.025 7.49e-05 40.253
SMC 2.1 5.172 4.66e-05 7.319
SMC 3.0 2.655 0.0143 2.061
SMC 4.0 1.063 0.295 0.300
SMC 10.0 -0.956 0.345 -0.279
SMC 50.0 0.307 0.761 0.116
Metro 2.1 6.432 1.21e-06 4.215
Metro 3.0 6.046 7.33e-06 12.189
Metro 4.0 4.516 0.000232 15.365
Metro 10.0 4.988 8.09e-05 27.645
Metro 50.0 5.166 5.46e-05 35.569
DEMetro_Z 2.1 4.909 9.48e-05 15.453
DEMetro_Z 3.0 4.870 0.000103 13.936
DEMetro_Z 4.0 5.053 6.89e-05 17.585
DEMetro_Z 10.0 8.635 4.84e-08 25.828
DEMetro_Z 50.0 4.777 0.00013 29.390
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.885 0.0748 -0.422
HMC_vs_DEMetro_Z 1 -0.420 0.679 -0.094
HMC_vs_DEMetro_Z 2 -0.348 0.732 -0.078
HMC_vs_DEMetro_Z 3 -1.008 0.326 -0.225
HMC_vs_DEMetro_Z 4 1.355 0.191 0.303
Metro_vs_SMC 0 -2.054 0.054 -0.459
Metro_vs_SMC 1 4.756 0.000137 1.064
Metro_vs_SMC 2 4.374 0.000326 0.978
Metro_vs_SMC 3 4.995 8.04e-05 1.117
Metro_vs_SMC 4 5.106 6.27e-05 1.142
Metro_vs_DEMetro_Z 0 -3.810 0.00118 -0.852
Metro_vs_DEMetro_Z 1 -0.606 0.552 -0.135
Metro_vs_DEMetro_Z 2 -0.426 0.675 -0.095
Metro_vs_DEMetro_Z 3 0.291 0.774 0.065
Metro_vs_DEMetro_Z 4 0.817 0.424 0.183
HMC_vs_Metro 0 3.653 0.00169 0.817
HMC_vs_Metro 1 0.035 0.972 0.008
HMC_vs_Metro 2 0.140 0.89 0.031
HMC_vs_Metro 3 -1.558 0.136 -0.348
HMC_vs_Metro 4 0.775 0.448 0.173
HMC_vs_SMC 0 1.090 0.289 0.244
HMC_vs_SMC 1 4.430 0.000288 0.991
HMC_vs_SMC 2 6.435 3.61e-06 1.439
HMC_vs_SMC 3 4.308 0.000379 0.963
HMC_vs_SMC 4 4.970 8.49e-05 1.111
DEMetro_Z_vs_SMC 0 2.625 0.0167 0.587
DEMetro_Z_vs_SMC 1 3.996 0.000774 0.893
DEMetro_Z_vs_SMC 2 5.011 7.77e-05 1.120
DEMetro_Z_vs_SMC 3 8.794 3.99e-08 1.966
DEMetro_Z_vs_SMC 4 4.706 0.000154 1.052
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.752 0.086 0.068 9.853
HMC 3.0 1.178 0.125 0.086 12.306
HMC 4.0 1.590 0.110 0.093 15.987
HMC 10.0 1.733 0.126 0.080 20.197
HMC 50.0 2.423 0.089 0.058 40.253
SMC 2.1 0.581 0.086 0.068 7.319
SMC 3.0 0.301 0.125 0.086 2.061
SMC 4.0 0.138 0.110 0.093 0.300
SMC 10.0 0.104 0.126 0.080 -0.279
SMC 50.0 0.096 0.089 0.058 0.116
Metro 2.1 0.371 0.086 0.068 4.215
Metro 3.0 1.168 0.125 0.086 12.189
Metro 4.0 1.533 0.110 0.093 15.365
Metro 10.0 2.325 0.126 0.080 27.645
Metro 50.0 2.152 0.089 0.058 35.569
DEMetro_Z 2.1 1.131 0.086 0.068 15.453
DEMetro_Z 3.0 1.318 0.125 0.086 13.936
DEMetro_Z 4.0 1.738 0.110 0.093 17.585
DEMetro_Z 10.0 2.181 0.126 0.080 25.828
DEMetro_Z 50.0 1.793 0.089 0.058 29.390
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.242 0.228 -0.283
HMC 3.0 3.694 0.00149 7.483
HMC 4.0 4.374 0.000324 22.837
HMC 10.0 3.357 0.00331 37.614
HMC 50.0 3.730 0.00142 78.671
SMC 2.1 -1.496 0.151 -0.335
SMC 3.0 2.309 0.0292 1.302
SMC 4.0 0.313 0.756 0.108
SMC 10.0 0.761 0.452 0.227
SMC 50.0 -0.325 0.747 -0.092
Metro 2.1 -1.571 0.133 -0.352
Metro 3.0 3.631 0.00175 10.857
Metro 4.0 2.861 0.01 27.602
Metro 10.0 3.489 0.00245 60.443
Metro 50.0 3.706 0.0015 59.948
DEMetro_Z 2.1 -1.181 0.251 -0.268
DEMetro_Z 3.0 3.590 0.00193 11.664
DEMetro_Z 4.0 3.372 0.0032 31.440
DEMetro_Z 10.0 5.731 1.58e-05 38.781
DEMetro_Z 50.0 2.618 0.0169 44.092
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.023 0.319 0.229
HMC_vs_SMC 1 2.850 0.0102 0.637
HMC_vs_SMC 2 4.353 0.000343 0.973
HMC_vs_SMC 3 3.372 0.0032 0.754
HMC_vs_SMC 4 3.740 0.00139 0.836
Metro_vs_DEMetro_Z 0 -2.486 0.0224 -0.556
Metro_vs_DEMetro_Z 1 -0.213 0.833 -0.048
Metro_vs_DEMetro_Z 2 -0.256 0.801 -0.057
Metro_vs_DEMetro_Z 3 1.182 0.252 0.264
Metro_vs_DEMetro_Z 4 0.717 0.482 0.160
HMC_vs_Metro 0 1.568 0.133 0.351
HMC_vs_Metro 1 -0.843 0.41 -0.189
HMC_vs_Metro 2 -0.422 0.678 -0.094
HMC_vs_Metro 3 -1.585 0.13 -0.354
HMC_vs_Metro 4 0.948 0.355 0.212
HMC_vs_DEMetro_Z 0 -0.292 0.773 -0.065
HMC_vs_DEMetro_Z 1 -0.981 0.339 -0.219
HMC_vs_DEMetro_Z 2 -0.737 0.47 -0.165
HMC_vs_DEMetro_Z 3 -0.085 0.934 -0.019
HMC_vs_DEMetro_Z 4 1.552 0.137 0.347
Metro_vs_SMC 0 -0.795 0.437 -0.178
Metro_vs_SMC 1 3.124 0.00558 0.699
Metro_vs_SMC 2 2.830 0.0107 0.633
Metro_vs_SMC 3 3.484 0.00248 0.779
Metro_vs_SMC 4 3.707 0.0015 0.829
DEMetro_Z_vs_SMC 0 1.698 0.106 0.380
DEMetro_Z_vs_SMC 1 3.127 0.00555 0.699
DEMetro_Z_vs_SMC 2 3.408 0.00295 0.762
DEMetro_Z_vs_SMC 3 5.697 1.72e-05 1.274
DEMetro_Z_vs_SMC 4 2.620 0.0169 0.586
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.424 17.896 40.526 -0.283
HMC 3.0 3.069 0.600 0.330 7.483
HMC 4.0 5.075 0.356 0.207 22.837
HMC 10.0 8.022 0.202 0.208 37.614
HMC 50.0 14.167 0.210 0.177 78.671
SMC 2.1 4.324 17.896 40.526 -0.335
SMC 3.0 1.029 0.600 0.330 1.302
SMC 4.0 0.378 0.356 0.207 0.108
SMC 10.0 0.250 0.202 0.208 0.227
SMC 50.0 0.193 0.210 0.177 -0.092
Metro 2.1 3.629 17.896 40.526 -0.352
Metro 3.0 4.182 0.600 0.330 10.857
Metro 4.0 6.060 0.356 0.207 27.602
Metro 10.0 12.768 0.202 0.208 60.443
Metro 50.0 10.846 0.210 0.177 59.948
DEMetro_Z 2.1 7.052 17.896 40.526 -0.268
DEMetro_Z 3.0 4.448 0.600 0.330 11.664
DEMetro_Z 4.0 6.853 0.356 0.207 31.440
DEMetro_Z 10.0 8.265 0.202 0.208 38.781
DEMetro_Z 50.0 8.033 0.210 0.177 44.092
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.976 7.21e-06 7.415
HMC 3.0 6.359 3.73e-06 12.369
HMC 4.0 6.375 3.83e-06 17.329
HMC 10.0 4.391 0.000312 22.928
HMC 50.0 5.020 7.57e-05 44.227
SMC 2.1 7.123 4.84e-07 6.890
SMC 3.0 3.125 0.00478 2.299
SMC 4.0 0.847 0.403 0.239
SMC 10.0 -1.013 0.318 -0.300
SMC 50.0 0.649 0.521 0.250
Metro 2.1 6.356 6.12e-07 3.034
Metro 3.0 6.423 3.26e-06 12.439
Metro 4.0 4.545 0.000218 16.179
Metro 10.0 4.761 0.000135 31.601
Metro 50.0 5.229 4.75e-05 38.803
DEMetro_Z 2.1 4.932 8.78e-05 11.275
DEMetro_Z 3.0 5.098 6.15e-05 14.254
DEMetro_Z 4.0 5.096 6.28e-05 19.089
DEMetro_Z 10.0 8.318 8.83e-08 29.997
DEMetro_Z 50.0 4.638 0.000179 31.959
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.789 0.00124 -0.847
Metro_vs_DEMetro_Z 1 -0.624 0.54 -0.139
Metro_vs_DEMetro_Z 2 -0.532 0.601 -0.119
Metro_vs_DEMetro_Z 3 0.218 0.83 0.049
Metro_vs_DEMetro_Z 4 0.812 0.427 0.181
DEMetro_Z_vs_SMC 0 1.886 0.0746 0.422
DEMetro_Z_vs_SMC 1 4.113 0.000592 0.920
DEMetro_Z_vs_SMC 2 5.079 6.66e-05 1.136
DEMetro_Z_vs_SMC 3 8.464 7.19e-08 1.893
DEMetro_Z_vs_SMC 4 4.553 0.000217 1.018
HMC_vs_DEMetro_Z 0 -1.788 0.0897 -0.400
HMC_vs_DEMetro_Z 1 -0.493 0.628 -0.110
HMC_vs_DEMetro_Z 2 -0.351 0.729 -0.079
HMC_vs_DEMetro_Z 3 -1.170 0.256 -0.262
HMC_vs_DEMetro_Z 4 1.374 0.185 0.307
HMC_vs_Metro 0 3.856 0.00106 0.862
HMC_vs_Metro 1 -0.022 0.982 -0.005
HMC_vs_Metro 2 0.244 0.81 0.055
HMC_vs_Metro 3 -1.536 0.141 -0.343
HMC_vs_Metro 4 0.787 0.441 0.176
HMC_vs_SMC 0 0.326 0.748 0.073
HMC_vs_SMC 1 4.581 0.000204 1.024
HMC_vs_SMC 2 6.350 4.3e-06 1.420
HMC_vs_SMC 3 4.424 0.000292 0.989
HMC_vs_SMC 4 4.949 8.91e-05 1.107
Metro_vs_SMC 0 -3.714 0.00147 -0.831
Metro_vs_SMC 1 4.983 8.26e-05 1.114
Metro_vs_SMC 2 4.419 0.000295 0.988
Metro_vs_SMC 3 4.766 0.000134 1.066
Metro_vs_SMC 4 5.145 5.75e-05 1.150
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.803 0.180 0.084 7.415
HMC 3.0 1.083 0.153 0.075 12.369
HMC 4.0 1.484 0.136 0.078 17.329
HMC 10.0 1.544 0.132 0.062 22.928
HMC 50.0 2.216 0.101 0.048 44.227
SMC 2.1 0.759 0.180 0.084 6.890
SMC 3.0 0.326 0.153 0.075 2.299
SMC 4.0 0.155 0.136 0.078 0.239
SMC 10.0 0.114 0.132 0.062 -0.300
SMC 50.0 0.113 0.101 0.048 0.250
Metro 2.1 0.435 0.180 0.084 3.034
Metro 3.0 1.088 0.153 0.075 12.439
Metro 4.0 1.394 0.136 0.078 16.179
Metro 10.0 2.078 0.132 0.062 31.601
Metro 50.0 1.957 0.101 0.048 38.803
DEMetro_Z 2.1 1.128 0.180 0.084 11.275
DEMetro_Z 3.0 1.225 0.153 0.075 14.254
DEMetro_Z 4.0 1.620 0.136 0.078 19.089
DEMetro_Z 10.0 1.979 0.132 0.062 29.997
DEMetro_Z 50.0 1.630 0.101 0.048 31.959
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.594 1.96e-05 11.037
HMC 3.0 5.812 1.26e-05 14.419
HMC 4.0 6.366 3.92e-06 17.764
HMC 10.0 4.376 0.000323 23.427
HMC 50.0 5.120 6.05e-05 39.589
SMC 2.1 5.889 9.49e-06 8.757
SMC 3.0 2.720 0.0125 2.266
SMC 4.0 0.857 0.397 0.241
SMC 10.0 -0.834 0.41 -0.238
SMC 50.0 0.255 0.8 0.090
Metro 2.1 6.319 2.04e-06 4.752
Metro 3.0 5.690 1.64e-05 14.080
Metro 4.0 4.493 0.000245 17.260
Metro 10.0 5.172 5.38e-05 31.428
Metro 50.0 5.223 4.81e-05 35.143
DEMetro_Z 2.1 4.597 0.000194 18.740
DEMetro_Z 3.0 4.712 0.000149 16.871
DEMetro_Z 4.0 5.137 5.74e-05 19.505
DEMetro_Z 10.0 8.746 4.06e-08 29.924
DEMetro_Z 50.0 4.951 8.81e-05 29.358
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 2.475 0.0229 0.553
DEMetro_Z_vs_SMC 1 3.966 0.000829 0.887
DEMetro_Z_vs_SMC 2 5.126 6e-05 1.146
DEMetro_Z_vs_SMC 3 8.864 3.54e-08 1.982
DEMetro_Z_vs_SMC 4 4.875 0.000105 1.090
HMC_vs_Metro 0 3.410 0.00294 0.762
HMC_vs_Metro 1 0.084 0.934 0.019
HMC_vs_Metro 2 0.102 0.92 0.023
HMC_vs_Metro 3 -1.553 0.137 -0.347
HMC_vs_Metro 4 0.793 0.438 0.177
Metro_vs_DEMetro_Z 0 -3.557 0.00211 -0.795
Metro_vs_DEMetro_Z 1 -0.799 0.434 -0.179
Metro_vs_DEMetro_Z 2 -0.391 0.7 -0.087
Metro_vs_DEMetro_Z 3 0.217 0.83 0.049
Metro_vs_DEMetro_Z 4 0.794 0.437 0.178
HMC_vs_SMC 0 0.869 0.396 0.194
HMC_vs_SMC 1 4.351 0.000344 0.973
HMC_vs_SMC 2 6.329 4.5e-06 1.415
HMC_vs_SMC 3 4.401 0.000307 0.984
HMC_vs_SMC 4 5.068 6.83e-05 1.133
Metro_vs_SMC 0 -2.448 0.0242 -0.547
Metro_vs_SMC 1 4.530 0.000229 1.013
Metro_vs_SMC 2 4.380 0.000322 0.979
Metro_vs_SMC 3 5.170 5.45e-05 1.156
Metro_vs_SMC 4 5.163 5.53e-05 1.154
HMC_vs_DEMetro_Z 0 -2.001 0.0599 -0.447
HMC_vs_DEMetro_Z 1 -0.517 0.611 -0.116
HMC_vs_DEMetro_Z 2 -0.344 0.735 -0.077
HMC_vs_DEMetro_Z 3 -1.032 0.315 -0.231
HMC_vs_DEMetro_Z 4 1.346 0.194 0.301
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.073 0.009 0.006 11.037
HMC 3.0 0.131 0.014 0.008 14.419
HMC 4.0 0.183 0.013 0.010 17.764
HMC 10.0 0.200 0.014 0.008 23.427
HMC 50.0 0.275 0.011 0.007 39.589
SMC 2.1 0.060 0.009 0.006 8.757
SMC 3.0 0.032 0.014 0.008 2.266
SMC 4.0 0.015 0.013 0.010 0.241
SMC 10.0 0.012 0.014 0.008 -0.238
SMC 50.0 0.011 0.011 0.007 0.090
Metro 2.1 0.037 0.009 0.006 4.752
Metro 3.0 0.128 0.014 0.008 14.080
Metro 4.0 0.178 0.013 0.010 17.260
Metro 10.0 0.263 0.014 0.008 31.428
Metro 50.0 0.245 0.011 0.007 35.143
DEMetro_Z 2.1 0.117 0.009 0.006 18.740
DEMetro_Z 3.0 0.151 0.014 0.008 16.871
DEMetro_Z 4.0 0.199 0.013 0.010 19.505
DEMetro_Z 10.0 0.251 0.014 0.008 29.924
DEMetro_Z 50.0 0.206 0.011 0.007 29.358
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.869 1.08e-05 12.270
HMC 3.0 5.338 3.55e-05 12.913
HMC 4.0 6.494 2.81e-06 12.620
HMC 10.0 20.410 1.79e-14 65.467
HMC 50.0 284.822 5.26e-64 96.381
SMC 2.1 5.062 6.37e-05 9.563
SMC 3.0 2.693 0.0116 1.252
SMC 4.0 0.640 0.526 0.195
SMC 10.0 -2.368 0.0237 -0.646
SMC 50.0 -0.132 0.896 -0.051
Metro 2.1 4.138 0.000447 3.689
Metro 3.0 3.132 0.00545 10.812
Metro 4.0 3.377 0.00315 15.272
Metro 10.0 12.217 1.82e-10 60.619
Metro 50.0 249.857 1.52e-57 96.327
DEMetro_Z 2.1 5.183 5.07e-05 13.871
DEMetro_Z 3.0 3.577 0.002 15.532
DEMetro_Z 4.0 4.966 8.5e-05 28.899
DEMetro_Z 10.0 5.898 1.11e-05 42.872
DEMetro_Z 50.0 7.601 3.53e-07 70.154
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.469 0.644 -0.105
HMC_vs_DEMetro_Z 1 -0.583 0.567 -0.130
HMC_vs_DEMetro_Z 2 -2.833 0.0106 -0.633
HMC_vs_DEMetro_Z 3 2.618 0.0169 0.585
HMC_vs_DEMetro_Z 4 2.872 0.00976 0.642
Metro_vs_SMC 0 -3.169 0.00505 -0.709
Metro_vs_SMC 1 2.695 0.0143 0.603
Metro_vs_SMC 2 3.357 0.00331 0.751
Metro_vs_SMC 3 12.388 1.51e-10 2.770
Metro_vs_SMC 4 254.702 4.89e-35 56.953
Metro_vs_DEMetro_Z 0 -3.846 0.00109 -0.860
Metro_vs_DEMetro_Z 1 -0.768 0.452 -0.172
Metro_vs_DEMetro_Z 2 -1.792 0.0891 -0.401
Metro_vs_DEMetro_Z 3 1.965 0.0642 0.439
Metro_vs_DEMetro_Z 4 2.887 0.00945 0.646
HMC_vs_Metro 0 3.399 0.00301 0.760
HMC_vs_Metro 1 0.519 0.61 0.116
HMC_vs_Metro 2 -0.542 0.594 -0.121
HMC_vs_Metro 3 0.825 0.419 0.185
HMC_vs_Metro 4 0.369 0.717 0.082
HMC_vs_SMC 0 0.806 0.43 0.180
HMC_vs_SMC 1 4.769 0.000134 1.066
HMC_vs_SMC 2 6.169 6.28e-06 1.379
HMC_vs_SMC 3 20.889 1.44e-14 4.671
HMC_vs_SMC 4 273.259 1.29e-35 61.103
DEMetro_Z_vs_SMC 0 1.229 0.234 0.275
DEMetro_Z_vs_SMC 1 3.307 0.00371 0.739
DEMetro_Z_vs_SMC 2 4.923 9.43e-05 1.101
DEMetro_Z_vs_SMC 3 5.998 9.01e-06 1.341
DEMetro_Z_vs_SMC 4 7.650 3.23e-07 1.711
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.915 0.086 0.068 12.270
HMC 3.0 1.230 0.125 0.086 12.913
HMC 4.0 1.279 0.110 0.093 12.620
HMC 10.0 5.334 0.126 0.080 65.467
HMC 50.0 5.678 0.089 0.058 96.381
SMC 2.1 0.732 0.086 0.068 9.563
SMC 3.0 0.232 0.125 0.086 1.252
SMC 4.0 0.129 0.110 0.093 0.195
SMC 10.0 0.075 0.126 0.080 -0.646
SMC 50.0 0.086 0.089 0.058 -0.051
Metro 2.1 0.335 0.086 0.068 3.689
Metro 3.0 1.050 0.125 0.086 10.812
Metro 4.0 1.524 0.110 0.093 15.272
Metro 10.0 4.948 0.126 0.080 60.619
Metro 50.0 5.675 0.089 0.058 96.327
DEMetro_Z 2.1 1.024 0.086 0.068 13.871
DEMetro_Z 3.0 1.455 0.125 0.086 15.532
DEMetro_Z 4.0 2.786 0.110 0.093 28.899
DEMetro_Z 10.0 3.537 0.126 0.080 42.872
DEMetro_Z 50.0 4.157 0.089 0.058 70.154
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.287 0.213 -0.293
HMC 3.0 3.616 0.00181 9.325
HMC 4.0 3.847 0.00107 13.753
HMC 10.0 17.532 3.39e-13 201.278
HMC 50.0 856.397 1.1e-81 253.958
SMC 2.1 -1.554 0.136 -0.348
SMC 3.0 0.455 0.652 0.204
SMC 4.0 -0.667 0.509 -0.205
SMC 10.0 -0.607 0.549 -0.155
SMC 50.0 -0.861 0.397 -0.219
Metro 2.1 -1.290 0.211 -0.300
Metro 3.0 2.395 0.027 12.462
Metro 4.0 2.275 0.0346 34.020
Metro 10.0 10.677 1.81e-09 185.080
Metro 50.0 858.300 1.29e-81 253.915
DEMetro_Z 2.1 -1.393 0.18 -0.312
DEMetro_Z 3.0 2.292 0.0335 20.640
DEMetro_Z 4.0 3.926 0.000906 88.950
DEMetro_Z 10.0 5.465 2.84e-05 129.224
DEMetro_Z 50.0 6.797 1.72e-06 178.852
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.424 0.171 0.318
HMC_vs_SMC 1 3.490 0.00245 0.780
HMC_vs_SMC 2 3.819 0.00116 0.854
HMC_vs_SMC 3 17.579 3.28e-13 3.931
HMC_vs_SMC 4 1609.079 3.02e-50 359.801
Metro_vs_DEMetro_Z 0 0.223 0.826 0.050
Metro_vs_DEMetro_Z 1 -0.734 0.472 -0.164
Metro_vs_DEMetro_Z 2 -2.010 0.0588 -0.449
Metro_vs_DEMetro_Z 3 1.851 0.0798 0.414
Metro_vs_DEMetro_Z 4 2.847 0.0103 0.637
HMC_vs_Metro 0 0.105 0.918 0.023
HMC_vs_Metro 1 -0.567 0.577 -0.127
HMC_vs_Metro 2 -1.377 0.185 -0.308
HMC_vs_Metro 3 0.829 0.417 0.185
HMC_vs_Metro 4 0.823 0.421 0.184
HMC_vs_DEMetro_Z 0 0.444 0.662 0.099
HMC_vs_DEMetro_Z 1 -1.278 0.217 -0.286
HMC_vs_DEMetro_Z 2 -3.482 0.0025 -0.779
HMC_vs_DEMetro_Z 3 2.497 0.0219 0.558
HMC_vs_DEMetro_Z 4 2.849 0.0103 0.637
Metro_vs_SMC 0 0.835 0.414 0.187
Metro_vs_SMC 1 2.349 0.0298 0.525
Metro_vs_SMC 2 2.305 0.0326 0.515
Metro_vs_SMC 3 10.693 1.77e-09 2.391
Metro_vs_SMC 4 1715.112 8.98e-51 383.511
DEMetro_Z_vs_SMC 0 2.682 0.0147 0.600
DEMetro_Z_vs_SMC 1 2.311 0.0322 0.517
DEMetro_Z_vs_SMC 2 3.921 0.000918 0.877
DEMetro_Z_vs_SMC 3 5.474 2.79e-05 1.224
DEMetro_Z_vs_SMC 4 6.802 1.71e-06 1.521
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.033 17.896 40.526 -0.293
HMC 3.0 3.677 0.600 0.330 9.325
HMC 4.0 3.198 0.356 0.207 13.753
HMC 10.0 42.046 0.202 0.208 201.278
HMC 50.0 45.267 0.210 0.177 253.958
SMC 2.1 3.774 17.896 40.526 -0.348
SMC 3.0 0.667 0.600 0.330 0.204
SMC 4.0 0.314 0.356 0.207 -0.205
SMC 10.0 0.170 0.202 0.208 -0.155
SMC 50.0 0.171 0.210 0.177 -0.219
Metro 2.1 5.735 17.896 40.526 -0.300
Metro 3.0 4.712 0.600 0.330 12.462
Metro 4.0 7.386 0.356 0.207 34.020
Metro 10.0 38.679 0.202 0.208 185.080
Metro 50.0 45.259 0.210 0.177 253.915
DEMetro_Z 2.1 5.240 17.896 40.526 -0.312
DEMetro_Z 3.0 7.410 0.600 0.330 20.640
DEMetro_Z 4.0 18.738 0.356 0.207 88.950
DEMetro_Z 10.0 27.067 0.202 0.208 129.224
DEMetro_Z 50.0 31.942 0.210 0.177 178.852
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.857 1.02e-05 8.663
HMC 3.0 5.305 3.84e-05 13.237
HMC 4.0 6.379 3.66e-06 13.647
HMC 10.0 18.639 1.02e-13 76.667
HMC 50.0 61.039 6.57e-24 102.675
SMC 2.1 5.370 2.99e-05 7.753
SMC 3.0 3.090 0.00429 1.399
SMC 4.0 0.243 0.81 0.076
SMC 10.0 -2.508 0.0171 -0.683
SMC 50.0 -0.287 0.776 -0.110
Metro 2.1 3.983 0.000628 3.277
Metro 3.0 3.232 0.00436 11.278
Metro 4.0 3.347 0.00337 15.992
Metro 10.0 11.866 3.03e-10 72.387
Metro 50.0 55.600 5.46e-23 104.811
DEMetro_Z 2.1 5.140 5.38e-05 9.984
DEMetro_Z 3.0 3.905 0.000942 15.341
DEMetro_Z 4.0 4.957 8.69e-05 31.966
DEMetro_Z 10.0 5.906 1.09e-05 48.056
DEMetro_Z 50.0 7.514 4.17e-07 76.192
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.318 0.00361 -0.742
Metro_vs_DEMetro_Z 1 -0.699 0.493 -0.156
Metro_vs_DEMetro_Z 2 -1.940 0.0673 -0.434
Metro_vs_DEMetro_Z 3 2.476 0.0229 0.554
Metro_vs_DEMetro_Z 4 2.681 0.0148 0.599
DEMetro_Z_vs_SMC 0 0.859 0.401 0.192
DEMetro_Z_vs_SMC 1 3.547 0.00215 0.793
DEMetro_Z_vs_SMC 2 4.933 9.24e-05 1.103
DEMetro_Z_vs_SMC 3 6.000 8.98e-06 1.342
DEMetro_Z_vs_SMC 4 7.553 3.9e-07 1.689
HMC_vs_DEMetro_Z 0 -0.536 0.598 -0.120
HMC_vs_DEMetro_Z 1 -0.481 0.636 -0.108
HMC_vs_DEMetro_Z 2 -2.917 0.00885 -0.652
HMC_vs_DEMetro_Z 3 2.959 0.00806 0.662
HMC_vs_DEMetro_Z 4 2.662 0.0154 0.595
HMC_vs_Metro 0 2.853 0.0102 0.638
HMC_vs_Metro 1 0.480 0.637 0.107
HMC_vs_Metro 2 -0.451 0.657 -0.101
HMC_vs_Metro 3 0.629 0.537 0.141
HMC_vs_Metro 4 -1.076 0.296 -0.241
HMC_vs_SMC 0 0.376 0.711 0.084
HMC_vs_SMC 1 4.662 0.00017 1.042
HMC_vs_SMC 2 6.113 7.07e-06 1.367
HMC_vs_SMC 3 18.928 8.65e-14 4.232
HMC_vs_SMC 4 66.903 5.07e-24 14.960
Metro_vs_SMC 0 -2.965 0.00795 -0.663
Metro_vs_SMC 1 2.756 0.0126 0.616
Metro_vs_SMC 2 3.375 0.00318 0.755
Metro_vs_SMC 3 12.007 2.56e-10 2.685
Metro_vs_SMC 4 55.526 1.72e-22 12.416
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.908 0.180 0.084 8.663
HMC 3.0 1.148 0.153 0.075 13.237
HMC 4.0 1.197 0.136 0.078 13.647
HMC 10.0 4.853 0.132 0.062 76.667
HMC 50.0 5.012 0.101 0.048 102.675
SMC 2.1 0.831 0.180 0.084 7.753
SMC 3.0 0.258 0.153 0.075 1.399
SMC 4.0 0.142 0.136 0.078 0.076
SMC 10.0 0.090 0.132 0.062 -0.683
SMC 50.0 0.096 0.101 0.048 -0.110
Metro 2.1 0.455 0.180 0.084 3.277
Metro 3.0 1.001 0.153 0.075 11.278
Metro 4.0 1.380 0.136 0.078 15.992
Metro 10.0 4.590 0.132 0.062 72.387
Metro 50.0 5.114 0.101 0.048 104.811
DEMetro_Z 2.1 1.019 0.180 0.084 9.984
DEMetro_Z 3.0 1.307 0.153 0.075 15.341
DEMetro_Z 4.0 2.622 0.136 0.078 31.966
DEMetro_Z 10.0 3.091 0.132 0.062 48.056
DEMetro_Z 50.0 3.745 0.101 0.048 76.192
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.544 2.27e-05 14.662
HMC 3.0 5.043 6.99e-05 14.993
HMC 4.0 6.319 4.17e-06 14.011
HMC 10.0 20.508 1.69e-14 71.187
HMC 50.0 110.039 1.41e-31 91.697
SMC 2.1 5.272 4.06e-05 11.389
SMC 3.0 2.796 0.00909 1.333
SMC 4.0 0.245 0.808 0.076
SMC 10.0 -2.440 0.02 -0.669
SMC 50.0 -0.225 0.824 -0.085
Metro 2.1 4.473 0.000194 3.820
Metro 3.0 3.077 0.00618 12.729
Metro 4.0 3.400 0.00299 15.957
Metro 10.0 12.182 1.92e-10 66.230
Metro 50.0 117.022 1.24e-32 91.872
DEMetro_Z 2.1 4.685 0.000158 16.424
DEMetro_Z 3.0 3.680 0.00158 18.245
DEMetro_Z 4.0 5.047 7.1e-05 31.077
DEMetro_Z 10.0 5.966 9.59e-06 47.214
DEMetro_Z 50.0 7.661 3.14e-07 66.771
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 1.144 0.267 0.256
DEMetro_Z_vs_SMC 1 3.418 0.00288 0.764
DEMetro_Z_vs_SMC 2 5.019 7.63e-05 1.122
DEMetro_Z_vs_SMC 3 6.060 7.91e-06 1.355
DEMetro_Z_vs_SMC 4 7.701 2.94e-07 1.722
HMC_vs_Metro 0 3.747 0.00137 0.838
HMC_vs_Metro 1 0.460 0.651 0.103
HMC_vs_Metro 2 -0.382 0.707 -0.085
HMC_vs_Metro 3 0.773 0.449 0.173
HMC_vs_Metro 4 -0.199 0.844 -0.045
Metro_vs_DEMetro_Z 0 -3.834 0.00112 -0.857
Metro_vs_DEMetro_Z 1 -0.772 0.45 -0.173
Metro_vs_DEMetro_Z 2 -1.903 0.0723 -0.425
Metro_vs_DEMetro_Z 3 1.928 0.069 0.431
Metro_vs_DEMetro_Z 4 2.938 0.00844 0.657
HMC_vs_SMC 0 0.813 0.426 0.182
HMC_vs_SMC 1 4.542 0.000223 1.016
HMC_vs_SMC 2 6.086 7.49e-06 1.361
HMC_vs_SMC 3 20.967 1.35e-14 4.688
HMC_vs_SMC 4 110.324 3.87e-28 24.669
Metro_vs_SMC 0 -3.573 0.00203 -0.799
Metro_vs_SMC 1 2.698 0.0142 0.603
Metro_vs_SMC 2 3.408 0.00295 0.762
Metro_vs_SMC 3 12.371 1.55e-10 2.766
Metro_vs_SMC 4 116.039 1.49e-28 25.947
HMC_vs_DEMetro_Z 0 -0.399 0.694 -0.089
HMC_vs_DEMetro_Z 1 -0.628 0.538 -0.140
HMC_vs_DEMetro_Z 2 -2.805 0.0113 -0.627
HMC_vs_DEMetro_Z 3 2.538 0.0201 0.567
HMC_vs_DEMetro_Z 4 2.816 0.011 0.630
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.093 0.009 0.006 14.662
HMC 3.0 0.136 0.014 0.008 14.993
HMC 4.0 0.147 0.013 0.010 14.011
HMC 10.0 0.579 0.014 0.008 71.187
HMC 50.0 0.622 0.011 0.007 91.697
SMC 2.1 0.075 0.009 0.006 11.389
SMC 3.0 0.024 0.014 0.008 1.333
SMC 4.0 0.014 0.013 0.010 0.076
SMC 10.0 0.008 0.014 0.008 -0.669
SMC 50.0 0.010 0.011 0.007 -0.085
Metro 2.1 0.031 0.009 0.006 3.820
Metro 3.0 0.117 0.014 0.008 12.729
Metro 4.0 0.165 0.013 0.010 15.957
Metro 10.0 0.540 0.014 0.008 66.230
Metro 50.0 0.624 0.011 0.007 91.872
DEMetro_Z 2.1 0.104 0.009 0.006 16.424
DEMetro_Z 3.0 0.162 0.014 0.008 18.245
DEMetro_Z 4.0 0.310 0.013 0.010 31.077
DEMetro_Z 10.0 0.389 0.014 0.008 47.214
DEMetro_Z 50.0 0.456 0.011 0.007 66.771
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Varying_Tails_with_high_Dimension_and_high_Correlation (MvStudentT, nu, 20 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.381 0.00282 3.383
HMC 3.0 3.768 0.00123 5.938
HMC 4.0 4.957 7e-05 5.511
HMC 10.0 5.534 1.25e-05 3.991
HMC 50.0 3.368 0.00274 2.664
SMC 2.1 78.276 2.45e-25 700.210
SMC 3.0 12.837 5.53e-11 23.673
SMC 4.0 15.311 3.32e-12 51.236
SMC 10.0 6.196 5.89e-06 44.674
SMC 50.0 13.264 4.68e-11 352.825
Metro 2.1 2.747 0.0128 608.155
Metro 3.0 4.287 0.000398 108.732
Metro 4.0 4.540 0.000224 227.346
Metro 10.0 6.633 2.4e-06 80.294
Metro 50.0 4.982 8.26e-05 51.647
DEMetro_Z 2.1 14.839 6.65e-12 937.201
DEMetro_Z 3.0 8.756 4.26e-08 209.731
DEMetro_Z 4.0 6.711 2.05e-06 349.114
DEMetro_Z 10.0 7.000 1.15e-06 169.990
DEMetro_Z 50.0 7.393 5.3e-07 196.491
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -14.822 6.79e-12 -3.314
HMC_vs_DEMetro_Z 1 -8.535 6.33e-08 -1.908
HMC_vs_DEMetro_Z 2 -6.614 2.5e-06 -1.479
HMC_vs_DEMetro_Z 3 -6.767 1.83e-06 -1.513
HMC_vs_DEMetro_Z 4 -7.284 6.56e-07 -1.629
Metro_vs_SMC 0 -0.415 0.683 -0.093
Metro_vs_SMC 1 3.403 0.00299 0.761
Metro_vs_SMC 2 3.507 0.00236 0.784
Metro_vs_SMC 3 2.314 0.032 0.517
Metro_vs_SMC 4 -9.220 1.91e-08 -2.062
Metro_vs_DEMetro_Z 0 -1.358 0.19 -0.304
Metro_vs_DEMetro_Z 1 -2.493 0.0221 -0.557
Metro_vs_DEMetro_Z 2 -1.700 0.105 -0.380
Metro_vs_DEMetro_Z 3 -3.513 0.00233 -0.786
Metro_vs_DEMetro_Z 4 -4.889 0.000102 -1.093
HMC_vs_Metro 0 -2.730 0.0133 -0.611
HMC_vs_Metro 1 -4.159 0.000533 -0.930
HMC_vs_Metro 2 -4.435 0.000284 -0.992
HMC_vs_Metro 3 -6.444 3.54e-06 -1.441
HMC_vs_Metro 4 -4.700 0.000156 -1.051
HMC_vs_SMC 0 -77.094 3.46e-25 -17.239
HMC_vs_SMC 1 -10.171 4e-09 -2.274
HMC_vs_SMC 2 -13.094 5.86e-11 -2.928
HMC_vs_SMC 3 -5.602 2.11e-05 -1.253
HMC_vs_SMC 4 -13.128 5.6e-11 -2.936
DEMetro_Z_vs_SMC 0 3.665 0.00165 0.819
DEMetro_Z_vs_SMC 1 7.805 2.41e-07 1.745
DEMetro_Z_vs_SMC 2 5.803 1.37e-05 1.298
DEMetro_Z_vs_SMC 3 4.585 0.000202 1.025
DEMetro_Z_vs_SMC 4 -4.870 0.000106 -1.089
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.188 0.069 0.035 3.383
HMC 3.0 0.145 0.032 0.019 5.938
HMC 4.0 0.106 0.026 0.015 5.511
HMC 10.0 0.076 0.021 0.014 3.991
HMC 50.0 0.050 0.019 0.012 2.664
SMC 2.1 24.649 0.069 0.035 700.210
SMC 3.0 0.480 0.032 0.019 23.673
SMC 4.0 0.769 0.026 0.015 51.236
SMC 10.0 0.637 0.021 0.014 44.674
SMC 50.0 4.182 0.019 0.012 352.825
Metro 2.1 21.417 0.069 0.035 608.155
Metro 3.0 2.086 0.032 0.019 108.732
Metro 4.0 3.323 0.026 0.015 227.346
Metro 10.0 1.128 0.021 0.014 80.294
Metro 50.0 0.628 0.019 0.012 51.647
DEMetro_Z 2.1 32.968 0.069 0.035 937.201
DEMetro_Z 3.0 3.994 0.032 0.019 209.731
DEMetro_Z 4.0 5.089 0.026 0.015 349.114
DEMetro_Z 10.0 2.365 0.021 0.014 169.990
DEMetro_Z 50.0 2.337 0.019 0.012 196.491
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.249 0.805 0.065
HMC 3.0 3.081 0.00532 2.273
HMC 4.0 4.161 0.000316 2.401
HMC 10.0 4.627 0.000155 5.454
HMC 50.0 4.354 0.00029 4.868
SMC 2.1 231.787 1.44e-34 711.610
SMC 3.0 264.712 1.83e-35 1383.760
SMC 4.0 200.568 4.52e-33 4616.389
SMC 10.0 35.532 7.66e-19 16720.900
SMC 50.0 110.292 3.89e-28 29098.775
Metro 2.1 1.612 0.123 714.282
Metro 3.0 2.649 0.0158 251.626
Metro 4.0 3.509 0.00235 550.263
Metro 10.0 5.339 3.75e-05 412.503
Metro 50.0 4.065 0.00066 76.597
DEMetro_Z 2.1 9.721 8.27e-09 210.856
DEMetro_Z 3.0 11.431 5.86e-10 420.084
DEMetro_Z 4.0 10.031 5.01e-09 1308.248
DEMetro_Z 10.0 8.850 3.63e-08 1959.442
DEMetro_Z 50.0 7.573 3.75e-07 1328.110
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -229.623 3.5e-34 -51.345
HMC_vs_SMC 1 -274.074 1.21e-35 -61.285
HMC_vs_SMC 2 -200.092 4.78e-33 -44.742
HMC_vs_SMC 3 -35.495 7.82e-19 -7.937
HMC_vs_SMC 4 -110.152 3.99e-28 -24.631
Metro_vs_DEMetro_Z 0 1.148 0.265 0.257
Metro_vs_DEMetro_Z 1 -1.727 0.1 -0.386
Metro_vs_DEMetro_Z 2 -3.456 0.00265 -0.773
Metro_vs_DEMetro_Z 3 -6.045 8.17e-06 -1.352
Metro_vs_DEMetro_Z 4 -7.151 8.51e-07 -1.599
HMC_vs_Metro 0 -1.612 0.123 -0.360
HMC_vs_Metro 1 -2.624 0.0167 -0.587
HMC_vs_Metro 2 -3.491 0.00244 -0.781
HMC_vs_Metro 3 -5.302 4.07e-05 -1.186
HMC_vs_Metro 4 -3.819 0.00116 -0.854
HMC_vs_DEMetro_Z 0 -9.715 8.37e-09 -2.172
HMC_vs_DEMetro_Z 1 -11.327 6.83e-10 -2.533
HMC_vs_DEMetro_Z 2 -10.015 5.14e-09 -2.239
HMC_vs_DEMetro_Z 3 -8.837 3.71e-08 -1.976
HMC_vs_DEMetro_Z 4 -7.556 3.87e-07 -1.690
Metro_vs_SMC 0 0.006 0.995 0.001
Metro_vs_SMC 1 -11.908 2.95e-10 -2.663
Metro_vs_SMC 2 -26.633 1.65e-16 -5.955
Metro_vs_SMC 3 -34.297 1.49e-18 -7.669
Metro_vs_SMC 4 -106.624 7.4e-28 -23.842
DEMetro_Z_vs_SMC 0 -21.851 6.33e-15 -4.886
DEMetro_Z_vs_SMC 1 -26.036 2.51e-16 -5.822
DEMetro_Z_vs_SMC 2 -24.605 7.15e-16 -5.502
DEMetro_Z_vs_SMC 3 -24.892 5.77e-16 -5.566
DEMetro_Z_vs_SMC 4 -85.768 4.59e-26 -19.178
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 5.975 5.195 11.992 0.065
HMC 3.0 1.030 0.411 0.273 2.273
HMC 4.0 0.357 0.147 0.088 2.401
HMC 10.0 0.117 0.034 0.015 5.454
HMC 50.0 0.123 0.034 0.018 4.868
SMC 2.1 8538.520 5.195 11.992 711.610
SMC 3.0 377.751 0.411 0.273 1383.760
SMC 4.0 404.424 0.147 0.088 4616.389
SMC 10.0 255.347 0.034 0.015 16720.900
SMC 50.0 529.036 0.034 0.018 29098.775
Metro 2.1 8570.566 5.195 11.992 714.282
Metro 3.0 69.027 0.411 0.273 251.626
Metro 4.0 48.336 0.147 0.088 550.263
Metro 10.0 6.332 0.034 0.015 412.503
Metro 50.0 1.427 0.034 0.018 76.597
DEMetro_Z 2.1 2533.696 5.195 11.992 210.856
DEMetro_Z 3.0 114.964 0.411 0.273 420.084
DEMetro_Z 4.0 114.716 0.147 0.088 1308.248
DEMetro_Z 10.0 29.953 0.034 0.015 1959.442
DEMetro_Z 50.0 24.178 0.034 0.018 1328.110
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.135 5.53e-05 11.236
HMC 3.0 7.051 9.1e-07 14.728
HMC 4.0 8.148 9.41e-08 12.624
HMC 10.0 9.525 2.72e-09 7.674
HMC 50.0 6.477 2.05e-06 6.531
SMC 2.1 288.955 4.14e-36 2852.097
SMC 3.0 312.978 7.06e-37 1478.715
SMC 4.0 280.045 7.08e-36 2055.262
SMC 10.0 59.812 4.19e-23 1465.435
SMC 50.0 82.192 1.02e-25 2818.752
Metro 2.1 4.625 0.000185 1304.580
Metro 3.0 5.528 2.48e-05 345.171
Metro 4.0 7.861 2.17e-07 505.115
Metro 10.0 7.854 2.2e-07 164.873
Metro 50.0 7.234 7.2e-07 97.896
DEMetro_Z 2.1 26.864 1.41e-16 1690.077
DEMetro_Z 3.0 22.342 4.21e-15 791.769
DEMetro_Z 4.0 17.831 2.54e-13 1094.837
DEMetro_Z 10.0 15.425 3.36e-12 477.915
DEMetro_Z 50.0 14.087 1.65e-11 493.987
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.391 0.18 -0.311
Metro_vs_DEMetro_Z 1 -5.678 1.79e-05 -1.270
Metro_vs_DEMetro_Z 2 -6.369 4.14e-06 -1.424
Metro_vs_DEMetro_Z 3 -8.229 1.1e-07 -1.840
Metro_vs_DEMetro_Z 4 -10.040 4.94e-09 -2.245
DEMetro_Z_vs_SMC 0 -18.107 1.92e-13 -4.049
DEMetro_Z_vs_SMC 1 -18.822 9.57e-14 -4.209
DEMetro_Z_vs_SMC 2 -15.439 3.31e-12 -3.452
DEMetro_Z_vs_SMC 3 -20.851 1.49e-14 -4.662
DEMetro_Z_vs_SMC 4 -50.682 9.63e-22 -11.333
HMC_vs_DEMetro_Z 0 -26.657 1.63e-16 -5.961
HMC_vs_DEMetro_Z 1 -21.526 8.33e-15 -4.813
HMC_vs_DEMetro_Z 2 -17.607 3.19e-13 -3.937
HMC_vs_DEMetro_Z 3 -14.999 5.51e-12 -3.354
HMC_vs_DEMetro_Z 4 -13.936 1.99e-11 -3.116
HMC_vs_Metro 0 -4.579 0.000205 -1.024
HMC_vs_Metro 1 -5.385 3.39e-05 -1.204
HMC_vs_Metro 2 -7.635 3.33e-07 -1.707
HMC_vs_Metro 3 -7.487 4.42e-07 -1.674
HMC_vs_Metro 4 -6.649 2.33e-06 -1.487
HMC_vs_SMC 0 -289.258 4.36e-36 -64.680
HMC_vs_SMC 1 -283.460 6.41e-36 -63.383
HMC_vs_SMC 2 -266.503 2.07e-35 -59.592
HMC_vs_SMC 3 -59.461 4.72e-23 -13.296
HMC_vs_SMC 4 -81.690 1.16e-25 -18.266
Metro_vs_SMC 0 -5.475 2.79e-05 -1.224
Metro_vs_SMC 1 -18.295 1.6e-13 -4.091
Metro_vs_SMC 2 -24.606 7.14e-16 -5.502
Metro_vs_SMC 3 -41.094 5e-20 -9.189
Metro_vs_SMC 4 -66.964 4.98e-24 -14.974
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.396 0.104 0.026 11.236
HMC 3.0 0.200 0.056 0.010 14.728
HMC 4.0 0.133 0.040 0.007 12.624
HMC 10.0 0.088 0.028 0.008 7.674
HMC 50.0 0.067 0.025 0.006 6.531
SMC 2.1 74.102 0.104 0.026 2852.097
SMC 3.0 14.492 0.056 0.010 1478.715
SMC 4.0 15.119 0.040 0.007 2055.262
SMC 10.0 11.398 0.028 0.008 1465.435
SMC 50.0 17.944 0.025 0.006 2818.752
Metro 2.1 33.952 0.104 0.026 1304.580
Metro 3.0 3.426 0.056 0.010 345.171
Metro 4.0 3.746 0.040 0.007 505.115
Metro 10.0 1.307 0.028 0.008 164.873
Metro 50.0 0.648 0.025 0.006 97.896
DEMetro_Z 2.1 43.953 0.104 0.026 1690.077
DEMetro_Z 3.0 7.786 0.056 0.010 791.769
DEMetro_Z 4.0 8.073 0.040 0.007 1094.837
DEMetro_Z 10.0 3.736 0.028 0.008 477.915
DEMetro_Z 50.0 3.166 0.025 0.006 493.987
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.485 3.72e-07 14.131
HMC 3.0 6.523 2.59e-06 11.793
HMC 4.0 6.514 2.6e-06 11.160
HMC 10.0 9.200 7.07e-09 8.527
HMC 50.0 5.908 7.3e-06 5.929
SMC 2.1 136.386 7.95e-38 79.751
SMC 3.0 158.470 6.3e-40 90.426
SMC 4.0 189.834 2.74e-40 118.552
SMC 10.0 68.112 1.08e-24 129.832
SMC 50.0 77.487 5.37e-26 125.597
Metro 2.1 53.870 1.34e-22 117.658
Metro 3.0 13.172 5.16e-11 99.609
Metro 4.0 15.963 1.8e-12 148.664
Metro 10.0 9.771 7.55e-09 91.348
Metro 50.0 10.696 1.71e-09 62.884
DEMetro_Z 2.1 40.903 3.6e-20 116.485
DEMetro_Z 3.0 44.761 6.21e-21 122.066
DEMetro_Z 4.0 24.717 6.22e-16 164.602
DEMetro_Z 10.0 33.112 2.3e-18 122.273
DEMetro_Z 50.0 31.027 7.79e-18 113.450
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 12.980 6.81e-11 2.902
DEMetro_Z_vs_SMC 1 11.621 4.44e-10 2.599
DEMetro_Z_vs_SMC 2 6.985 1.18e-06 1.562
DEMetro_Z_vs_SMC 3 -1.635 0.119 -0.366
DEMetro_Z_vs_SMC 4 -3.177 0.00496 -0.710
HMC_vs_Metro 0 -45.609 7.04e-21 -10.198
HMC_vs_Metro 1 -12.340 1.61e-10 -2.759
HMC_vs_Metro 2 -14.777 7.16e-12 -3.304
HMC_vs_Metro 3 -8.811 3.88e-08 -1.970
HMC_vs_Metro 4 -9.526 1.14e-08 -2.130
Metro_vs_DEMetro_Z 0 0.310 0.76 0.069
Metro_vs_DEMetro_Z 1 -2.603 0.0175 -0.582
Metro_vs_DEMetro_Z 2 -1.647 0.116 -0.368
Metro_vs_DEMetro_Z 3 -2.961 0.00802 -0.662
Metro_vs_DEMetro_Z 4 -7.104 9.34e-07 -1.588
HMC_vs_SMC 0 -31.678 6.56e-18 -7.083
HMC_vs_SMC 1 -40.761 5.83e-20 -9.114
HMC_vs_SMC 2 -57.604 8.59e-23 -12.881
HMC_vs_SMC 3 -58.850 5.73e-23 -13.159
HMC_vs_SMC 4 -62.843 1.66e-23 -14.052
Metro_vs_SMC 0 15.508 3.06e-12 3.468
Metro_vs_SMC 1 1.181 0.252 0.264
Metro_vs_SMC 2 3.205 0.00466 0.717
Metro_vs_SMC 3 -4.111 0.000595 -0.919
Metro_vs_SMC 4 -9.497 1.2e-08 -2.124
HMC_vs_DEMetro_Z 0 -30.433 1.39e-17 -6.805
HMC_vs_DEMetro_Z 1 -35.301 8.66e-19 -7.894
HMC_vs_DEMetro_Z 2 -23.587 1.56e-15 -5.274
HMC_vs_DEMetro_Z 3 -29.266 2.87e-17 -6.544
HMC_vs_DEMetro_Z 4 -32.132 5.03e-18 -7.185
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.094 0.017 0.005 14.131
HMC 3.0 0.069 0.015 0.005 11.793
HMC 4.0 0.054 0.014 0.004 11.160
HMC 10.0 0.052 0.013 0.005 8.527
HMC 50.0 0.044 0.014 0.005 5.929
SMC 2.1 0.452 0.017 0.005 79.751
SMC 3.0 0.431 0.015 0.005 90.426
SMC 4.0 0.439 0.014 0.004 118.552
SMC 10.0 0.610 0.013 0.005 129.832
SMC 50.0 0.649 0.014 0.005 125.597
Metro 2.1 0.658 0.017 0.005 117.658
Metro 3.0 0.473 0.015 0.005 99.609
Metro 4.0 0.547 0.014 0.004 148.664
Metro 10.0 0.433 0.013 0.005 91.348
Metro 50.0 0.332 0.014 0.005 62.884
DEMetro_Z 2.1 0.652 0.017 0.005 116.485
DEMetro_Z 3.0 0.576 0.015 0.005 122.066
DEMetro_Z 4.0 0.604 0.014 0.004 164.602
DEMetro_Z 10.0 0.576 0.013 0.005 122.273
DEMetro_Z 50.0 0.588 0.014 0.005 113.450
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.154 0.0431 2.216
HMC 3.0 3.097 0.00583 6.951
HMC 4.0 4.792 0.000122 12.133
HMC 10.0 4.946 7.71e-05 6.712
HMC 50.0 3.912 0.000889 6.771
SMC 2.1 45.203 8.2e-21 678.647
SMC 3.0 12.414 1.09e-10 26.160
SMC 4.0 7.646 3.23e-07 63.664
SMC 10.0 5.385 3.38e-05 53.247
SMC 50.0 18.684 1.09e-13 424.228
Metro 2.1 6.190 6.01e-06 481.010
Metro 3.0 4.023 0.000728 226.850
Metro 4.0 4.562 0.000213 156.847
Metro 10.0 3.772 0.00129 124.463
Metro 50.0 4.405 0.000304 38.274
DEMetro_Z 2.1 7.503 4.29e-07 923.588
DEMetro_Z 3.0 6.607 2.53e-06 421.732
DEMetro_Z 4.0 4.249 0.000434 440.191
DEMetro_Z 10.0 4.339 0.000353 282.374
DEMetro_Z 50.0 5.133 5.91e-05 352.496
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -7.483 4.45e-07 -1.673
HMC_vs_DEMetro_Z 1 -6.566 2.76e-06 -1.468
HMC_vs_DEMetro_Z 2 -4.163 0.000528 -0.931
HMC_vs_DEMetro_Z 3 -4.235 0.000448 -0.947
HMC_vs_DEMetro_Z 4 -4.993 8.07e-05 -1.117
Metro_vs_SMC 0 -2.603 0.0175 -0.582
Metro_vs_SMC 1 3.572 0.00204 0.799
Metro_vs_SMC 2 2.560 0.0191 0.572
Metro_vs_SMC 3 2.079 0.0514 0.465
Metro_vs_SMC 4 -14.531 9.61e-12 -3.249
Metro_vs_DEMetro_Z 0 -3.514 0.00232 -0.786
Metro_vs_DEMetro_Z 1 -3.374 0.00319 -0.754
Metro_vs_DEMetro_Z 2 -2.529 0.0204 -0.566
Metro_vs_DEMetro_Z 3 -2.191 0.0411 -0.490
Metro_vs_DEMetro_Z 4 -4.789 0.000128 -1.071
HMC_vs_Metro 0 -6.151 6.52e-06 -1.375
HMC_vs_Metro 1 -4.021 0.000729 -0.899
HMC_vs_Metro 2 -4.232 0.000451 -0.946
HMC_vs_Metro 3 -3.553 0.00212 -0.794
HMC_vs_Metro 4 -3.575 0.00202 -0.799
HMC_vs_SMC 0 -45.529 7.27e-21 -10.181
HMC_vs_SMC 1 -5.955 9.88e-06 -1.332
HMC_vs_SMC 2 -6.197 5.92e-06 -1.386
HMC_vs_SMC 3 -4.812 0.000121 -1.076
HMC_vs_SMC 4 -18.105 1.93e-13 -4.048
DEMetro_Z_vs_SMC 0 1.925 0.0694 0.430
DEMetro_Z_vs_SMC 1 6.241 5.41e-06 1.395
DEMetro_Z_vs_SMC 2 3.558 0.0021 0.796
DEMetro_Z_vs_SMC 3 3.337 0.00346 0.746
DEMetro_Z_vs_SMC 4 -1.004 0.328 -0.225
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.147 0.069 0.035 2.216
HMC 3.0 0.164 0.032 0.019 6.951
HMC 4.0 0.202 0.026 0.015 12.133
HMC 10.0 0.113 0.021 0.014 6.712
HMC 50.0 0.099 0.019 0.012 6.771
SMC 2.1 23.892 0.069 0.035 678.647
SMC 3.0 0.527 0.032 0.019 26.160
SMC 4.0 0.949 0.026 0.015 63.664
SMC 10.0 0.755 0.021 0.014 53.247
SMC 50.0 5.025 0.019 0.012 424.228
Metro 2.1 16.954 0.069 0.035 481.010
Metro 3.0 4.317 0.032 0.019 226.850
Metro 4.0 2.301 0.026 0.015 156.847
Metro 10.0 1.737 0.021 0.014 124.463
Metro 50.0 0.470 0.019 0.012 38.274
DEMetro_Z 2.1 32.490 0.069 0.035 923.588
DEMetro_Z 3.0 7.999 0.032 0.019 421.732
DEMetro_Z 4.0 6.410 0.026 0.015 440.191
DEMetro_Z 10.0 3.915 0.021 0.014 282.374
DEMetro_Z 50.0 4.178 0.019 0.012 352.496
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.139 0.891 0.034
HMC 3.0 1.744 0.0973 6.223
HMC 4.0 3.168 0.00495 6.190
HMC 10.0 4.540 0.000206 7.493
HMC 50.0 3.582 0.00176 3.578
SMC 2.1 205.575 1.77e-33 751.836
SMC 3.0 221.164 6.16e-34 1474.317
SMC 4.0 134.404 9.1e-30 4988.564
SMC 10.0 139.009 4.82e-30 26405.446
SMC 50.0 101.698 1.81e-27 31105.324
Metro 2.1 1.734 0.0992 87.843
Metro 3.0 1.236 0.231 176.870
Metro 4.0 1.694 0.107 96.537
Metro 10.0 2.477 0.0228 175.957
Metro 50.0 4.318 0.000369 28.844
DEMetro_Z 2.1 13.773 2.23e-11 54.369
DEMetro_Z 3.0 10.778 1.52e-09 73.256
DEMetro_Z 4.0 9.140 2.19e-08 220.699
DEMetro_Z 10.0 11.044 1.04e-09 209.484
DEMetro_Z 50.0 4.314 0.000374 89.004
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -206.220 2.7e-33 -46.112
HMC_vs_SMC 1 -195.611 7.35e-33 -43.740
HMC_vs_SMC 2 -132.551 1.19e-29 -29.639
HMC_vs_SMC 3 -138.873 4.91e-30 -31.053
HMC_vs_SMC 4 -101.558 1.86e-27 -22.709
Metro_vs_DEMetro_Z 0 0.660 0.517 0.148
Metro_vs_DEMetro_Z 1 0.734 0.472 0.164
Metro_vs_DEMetro_Z 2 -1.893 0.0736 -0.423
Metro_vs_DEMetro_Z 3 -0.484 0.634 -0.108
Metro_vs_DEMetro_Z 4 -2.584 0.0182 -0.578
HMC_vs_Metro 0 -1.733 0.0993 -0.387
HMC_vs_Metro 1 -1.221 0.237 -0.273
HMC_vs_Metro 2 -1.578 0.131 -0.353
HMC_vs_Metro 3 -2.362 0.029 -0.528
HMC_vs_Metro 4 -3.723 0.00144 -0.833
HMC_vs_DEMetro_Z 0 -13.738 2.56e-11 -3.072
HMC_vs_DEMetro_Z 1 -10.507 2.36e-09 -2.349
HMC_vs_DEMetro_Z 2 -8.998 2.8e-08 -2.012
HMC_vs_DEMetro_Z 3 -10.437 2.63e-09 -2.334
HMC_vs_DEMetro_Z 4 -4.130 0.000569 -0.924
Metro_vs_SMC 0 -13.122 5.65e-11 -2.934
Metro_vs_SMC 1 -9.069 2.48e-08 -2.028
Metro_vs_SMC 2 -79.456 1.95e-25 -17.767
Metro_vs_SMC 3 -146.364 1.81e-30 -32.728
Metro_vs_SMC 4 -101.339 1.94e-27 -22.660
DEMetro_Z_vs_SMC 0 -157.766 4.36e-31 -35.278
DEMetro_Z_vs_SMC 1 -162.516 2.48e-31 -36.340
DEMetro_Z_vs_SMC 2 -106.688 7.32e-28 -23.856
DEMetro_Z_vs_SMC 3 -140.819 3.77e-30 -31.488
DEMetro_Z_vs_SMC 4 -100.837 2.13e-27 -22.548
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 5.605 5.195 11.992 0.034
HMC 3.0 2.107 0.411 0.273 6.223
HMC 4.0 0.689 0.147 0.088 6.190
HMC 10.0 0.148 0.034 0.015 7.493
HMC 50.0 0.099 0.034 0.018 3.578
SMC 2.1 9020.891 5.195 11.992 751.836
SMC 3.0 402.445 0.411 0.273 1474.317
SMC 4.0 437.017 0.147 0.088 4988.564
SMC 10.0 403.222 0.034 0.015 26405.446
SMC 50.0 565.514 0.034 0.018 31105.324
Metro 2.1 1058.567 5.195 11.992 87.843
Metro 3.0 48.642 0.411 0.273 176.870
Metro 4.0 8.601 0.147 0.088 96.537
Metro 10.0 2.721 0.034 0.015 175.957
Metro 50.0 0.558 0.034 0.018 28.844
DEMetro_Z 2.1 657.163 5.195 11.992 54.369
DEMetro_Z 3.0 20.387 0.411 0.273 73.256
DEMetro_Z 4.0 19.474 0.147 0.088 220.699
DEMetro_Z 10.0 3.232 0.034 0.015 209.484
DEMetro_Z 50.0 1.652 0.034 0.018 89.004
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 6.381 3.05e-06 8.311
HMC 3.0 4.873 0.000103 15.145
HMC 4.0 5.676 1.75e-05 20.573
HMC 10.0 6.308 3.97e-06 10.461
HMC 50.0 4.705 0.000147 10.903
SMC 2.1 228.586 3.66e-34 2902.725
SMC 3.0 247.518 7.04e-35 1521.573
SMC 4.0 181.013 3.07e-32 2113.543
SMC 10.0 105.896 8.29e-28 1902.547
SMC 50.0 103.544 1.28e-27 2937.294
Metro 2.1 6.165 6.34e-06 565.941
Metro 3.0 4.148 0.000547 369.132
Metro 4.0 4.696 0.000157 263.806
Metro 10.0 3.832 0.00113 184.059
Metro 50.0 5.165 5.49e-05 62.974
DEMetro_Z 2.1 11.778 3.55e-10 1263.176
DEMetro_Z 3.0 7.710 2.89e-07 754.191
DEMetro_Z 4.0 5.238 4.68e-05 814.335
DEMetro_Z 10.0 4.740 0.000143 435.807
DEMetro_Z 50.0 5.406 3.24e-05 546.338
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -5.983 9.32e-06 -1.338
Metro_vs_DEMetro_Z 1 -4.366 0.000332 -0.976
Metro_vs_DEMetro_Z 2 -3.255 0.00417 -0.728
Metro_vs_DEMetro_Z 3 -2.430 0.0252 -0.543
Metro_vs_DEMetro_Z 4 -5.001 7.94e-05 -1.118
DEMetro_Z_vs_SMC 0 -15.140 4.67e-12 -3.385
DEMetro_Z_vs_SMC 1 -7.826 2.32e-07 -1.750
DEMetro_Z_vs_SMC 2 -8.046 1.54e-07 -1.799
DEMetro_Z_vs_SMC 3 -15.469 3.2e-12 -3.459
DEMetro_Z_vs_SMC 4 -20.581 1.89e-14 -4.602
HMC_vs_DEMetro_Z 0 -11.670 4.14e-10 -2.610
HMC_vs_DEMetro_Z 1 -7.658 3.19e-07 -1.712
HMC_vs_DEMetro_Z 2 -5.144 5.77e-05 -1.150
HMC_vs_DEMetro_Z 3 -4.619 0.000187 -1.033
HMC_vs_DEMetro_Z 4 -5.270 4.36e-05 -1.178
HMC_vs_Metro 0 -6.045 8.16e-06 -1.352
HMC_vs_Metro 1 -4.081 0.000636 -0.913
HMC_vs_Metro 2 -4.346 0.000348 -0.972
HMC_vs_Metro 3 -3.599 0.00191 -0.805
HMC_vs_Metro 4 -4.249 0.000434 -0.950
HMC_vs_SMC 0 -229.215 3.62e-34 -51.254
HMC_vs_SMC 1 -214.092 1.32e-33 -47.872
HMC_vs_SMC 2 -169.732 1.09e-31 -37.953
HMC_vs_SMC 3 -110.031 4.07e-28 -24.604
HMC_vs_SMC 4 -102.123 1.68e-27 -22.835
Metro_vs_SMC 0 -26.765 1.51e-16 -5.985
Metro_vs_SMC 1 -12.787 8.79e-11 -2.859
Metro_vs_SMC 2 -32.689 3.65e-18 -7.310
Metro_vs_SMC 3 -35.717 6.96e-19 -7.986
Metro_vs_SMC 4 -87.504 3.14e-26 -19.567
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.320 0.104 0.026 8.311
HMC 3.0 0.204 0.056 0.010 15.145
HMC 4.0 0.191 0.040 0.007 20.573
HMC 10.0 0.109 0.028 0.008 10.461
HMC 50.0 0.095 0.025 0.006 10.903
SMC 2.1 75.416 0.104 0.026 2902.725
SMC 3.0 14.910 0.056 0.010 1521.573
SMC 4.0 15.547 0.040 0.007 2113.543
SMC 10.0 14.790 0.028 0.008 1902.547
SMC 50.0 18.697 0.025 0.006 2937.294
Metro 2.1 14.788 0.104 0.026 565.941
Metro 3.0 3.660 0.056 0.010 369.132
Metro 4.0 1.976 0.040 0.007 263.806
Metro 10.0 1.456 0.028 0.008 184.059
Metro 50.0 0.426 0.025 0.006 62.974
DEMetro_Z 2.1 32.877 0.104 0.026 1263.176
DEMetro_Z 3.0 7.419 0.056 0.010 754.191
DEMetro_Z 4.0 6.015 0.040 0.007 814.335
DEMetro_Z 10.0 3.410 0.028 0.008 435.807
DEMetro_Z 50.0 3.498 0.025 0.006 546.338
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 8.743 2.33e-08 9.939
HMC 3.0 10.609 4.43e-10 8.981
HMC 4.0 6.721 1.77e-06 13.463
HMC 10.0 7.531 2.72e-07 9.496
HMC 50.0 5.039 6.49e-05 7.971
SMC 2.1 97.730 2.79e-30 83.473
SMC 3.0 105.945 1.06e-30 95.454
SMC 4.0 90.356 1.25e-27 124.487
SMC 10.0 72.695 3.15e-25 140.363
SMC 50.0 99.260 1.08e-28 124.531
Metro 2.1 20.554 1.84e-14 129.405
Metro 3.0 12.670 1.02e-10 137.012
Metro 4.0 10.855 1.37e-09 149.095
Metro 10.0 8.306 9.51e-08 96.213
Metro 50.0 7.611 3.42e-07 44.993
DEMetro_Z 2.1 20.569 1.82e-14 134.959
DEMetro_Z 3.0 15.804 2.16e-12 167.826
DEMetro_Z 4.0 14.405 1.11e-11 190.936
DEMetro_Z 10.0 11.619 4.43e-10 160.346
DEMetro_Z 50.0 13.388 3.96e-11 162.428
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.883 2.09e-07 1.763
DEMetro_Z_vs_SMC 1 6.745 1.91e-06 1.508
DEMetro_Z_vs_SMC 2 5.138 5.85e-05 1.149
DEMetro_Z_vs_SMC 3 1.519 0.145 0.340
DEMetro_Z_vs_SMC 4 3.207 0.00464 0.717
HMC_vs_Metro 0 -18.805 9.73e-14 -4.205
HMC_vs_Metro 1 -11.877 3.08e-10 -2.656
HMC_vs_Metro 2 -9.655 9.24e-09 -2.159
HMC_vs_Metro 3 -7.570 3.77e-07 -1.693
HMC_vs_Metro 4 -6.368 4.15e-06 -1.424
Metro_vs_DEMetro_Z 0 -0.677 0.507 -0.151
Metro_vs_DEMetro_Z 1 -2.893 0.00932 -0.647
Metro_vs_DEMetro_Z 2 -2.061 0.0533 -0.461
Metro_vs_DEMetro_Z 3 -3.840 0.0011 -0.859
Metro_vs_DEMetro_Z 4 -8.614 5.5e-08 -1.926
HMC_vs_SMC 0 -49.022 1.81e-21 -10.962
HMC_vs_SMC 1 -72.405 1.14e-24 -16.190
HMC_vs_SMC 2 -44.804 9.84e-21 -10.019
HMC_vs_SMC 3 -60.829 3.07e-23 -13.602
HMC_vs_SMC 4 -50.202 1.15e-21 -11.226
Metro_vs_SMC 0 7.582 3.69e-07 1.695
Metro_vs_SMC 1 3.858 0.00106 0.863
Metro_vs_SMC 2 1.722 0.101 0.385
Metro_vs_SMC 3 -3.659 0.00167 -0.818
Metro_vs_SMC 4 -13.087 5.91e-11 -2.926
HMC_vs_DEMetro_Z 0 -18.490 1.32e-13 -4.135
HMC_vs_DEMetro_Z 1 -15.050 5.19e-12 -3.365
HMC_vs_DEMetro_Z 2 -12.904 7.52e-11 -2.885
HMC_vs_DEMetro_Z 3 -10.905 1.28e-09 -2.438
HMC_vs_DEMetro_Z 4 -12.325 1.65e-10 -2.756
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.071 0.017 0.005 9.939
HMC 3.0 0.056 0.015 0.005 8.981
HMC 4.0 0.062 0.014 0.004 13.463
HMC 10.0 0.057 0.013 0.005 9.496
HMC 50.0 0.054 0.014 0.005 7.971
SMC 2.1 0.472 0.017 0.005 83.473
SMC 3.0 0.454 0.015 0.005 95.454
SMC 4.0 0.460 0.014 0.004 124.487
SMC 10.0 0.659 0.013 0.005 140.363
SMC 50.0 0.644 0.014 0.005 124.531
Metro 2.1 0.722 0.017 0.005 129.405
Metro 3.0 0.645 0.015 0.005 137.012
Metro 4.0 0.549 0.014 0.004 149.095
Metro 10.0 0.456 0.013 0.005 96.213
Metro 50.0 0.242 0.014 0.005 44.993
DEMetro_Z 2.1 0.753 0.017 0.005 134.959
DEMetro_Z 3.0 0.787 0.015 0.005 167.826
DEMetro_Z 4.0 0.699 0.014 0.004 190.936
DEMetro_Z 10.0 0.751 0.013 0.005 160.346
DEMetro_Z 50.0 0.835 0.014 0.005 162.428
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess Per Sec
ess_per_sec plot
R Hat
r_hat plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50